Protecting images with an image watermark

ABSTRACT

A robust means of watermarking a digitized image with a highly random sequence of pixel brightness multipliers is presented. The random sequence is formed from ‘robust-watermarking-parameters’ selected and known only by the marker and/or the marking entity. A watermarking plane is generated having an element array with one-to-one element positional correspondence with the pixels of the digitized image being marked. Each element of the watermarking plane is assigned a random value dependent upon a robust random sequence and a specified brightness modulation strength. The so generated watermarking plane is imparted onto the digitized image by multiplying the brightness value or values of each pixel by its corresponding element value in the watermarking plane. The resulting modified brightness values impart the random and relatively invisible watermark onto the digitized image. Brightness modulation is the essence of watermark imparting. Detection of an imparted watermark requires knowing the watermarking plane with which the watermark was imparted. Regeneration of the watermarking plane requires knowledge of the robust-marking-parameters used in its formulation. This is generally only known to the marker and/or marking entity. Once regenerated, the watermarking plane is used together with a verifying image located in a ‘visualizer’ to demonstrate the existence of the watermark. The process of watermark detection is enhanced by application of a blurring filter to the marked image before detection is attempted.

FIELD OF THE INVENTION

[0001] This application relates to the field of digital imaging. It ismore specifically concerned with the insertion and detection of anidentifying mark on a work-piece.

BACKGROUND OF THE INVENTION

[0002] It is a constant endeavor to find improved techniques of placinga visible or invisible identifying mark on an image. This is generallyuseful to establish ownership, origin and authenticity, and also todiscourage those who might wish to purloin or misappropriate the work.Identifying marks are also useful to give evidence of unauthorizedalteration or disclosure. Visible marks are herein classified as beingeither visible robust or visible fragile. A mark is classified asvisible robust if it can be seen by the unaided eye and cannot be easilyremoved from the work-piece, if at all, without leaving telltaleevidence. It is classified as visible fragile if the mark itself isvisibly altered by an attempt to alter the work-piece or its wrapper.

[0003] Invisible marks are herein classified relative to the appearanceof that mark to a human being with normal visual acuity. A mark on animage is classified as having an invisibility classification level ofundetectably invisible if, when the image without the marking isdisplayed together with an image copy with the marking, the human beingis equally likely to select either of these copies. An undetectablyinvisible mark is below or at the human being's just noticeabledifference. A mark on an image is classified as having an invisibilityclassification level of subliminally invisible if the mark is notdistracting to the human viewer, although it is above the human being'sjust noticeable difference. An image mark is classified as beingmarginally invisible if it does not cause the marked image to lose itsusefulness or value because of the mark. An image marking is classifiedas being poorly invisible if the marking causes a reduction in theusefulness and/or value of the image.

[0004] Presently, both visible and invisible markings of hardcopydocuments are used as a generally dependable method of establishingownership and authenticity. These time-tested methods are also usefulfor marking a “softcopy” digitized image, also referred to herein as animage. A digitized image is an abstraction of a physical image that hasbeen scanned and stored in a computer's memory as rectangular arrays ofnumbers corresponding to that image's (one or more) color planes. Eacharray element corresponding to a very small area of the physical imageis called a picture element, or pixel. The numeric value associated witheach pixel for a monochrome image represents the magnitude of itsaverage brightness on its single color (black and white) plane. For acolor image, each pixel has values associated and representing themagnitude or average brightness of its tristimulus color componentsrepresenting its three color planes. Other image representations havemore than three color components for each pixel. A different componentvalue is associated with each different one of the image's color planes.

[0005] In what follows, whenever reference is made to color planes it isunderstood to include any number of color planes used by a particularimage's digitizing technique to define the pixel's colorcharacteristics. This includes the case when there is only a singleplane defining a monochrome image.

[0006] A digitized image is recognizable as an image to a human vieweronly when the individual pixels are displayed as dots of white orcolored light on a display or as dots of black or colored inks or dyeson a hardcopy. Pixels are normally spaced so closely as to beunresolvable by the human visual system. This results in the fusion ofneighboring pixels by the human visual system into a representation ofthe original physical image. Image fusion by the human visual systemmakes invisible marking, or relatively invisible marking, of imagespossible. This property is fully exploited by the methods described hereto both impart upon a digitized image an invisible watermark to adesired invisibility classification, and to subsequently demonstrate itsexistence. The imparting and demonstrated detection of a robustinvisible marking on digitized images, herein called invisiblewatermarking, are a primary aspect of the present invention.

[0007] Properties of a Robust Invisible Watermark

[0008] A proper invisible watermarking technique that imparts aninvisible watermark upon a proprietary digitized image should satisfyseveral properties. The imparted watermark should appear to be invisibleto any person having normal or corrected visual accommodation to adesired invisibility classification level. Clearly, the degree ofmarking is a dichotomy. A balance has to be struck between protectingthe image from unauthorized uses and not having the watermarkunpleasantly alter the appearance of the image. This generally meansthat a recognizable pattern should not appear in the marked image whenthe watermark is applied to a uniform color plane. This requirementdiscourages marking the image by varying the hue of its pixels, sincethe human visual system is significantly more sensitive to alterationsin hue than in brightness. The requirement can be satisfied by atechnique based on varying pixel brightness implemented in a proper way.A technique based on varying pixel brightness also allows the samemarking technique applied to color images to be equally applicable tomonochrome images.

[0009] Another property of a proper invisible watermarking technique isthat it should have a detection scheme such that the probability of afalse-positive detection is vanishingly small. For purposes of thepresent invention, the probability of detection of a watermark in animage when one does not exist should be less than one in a million.There is generally little difficulty satisfying this requirement whenthe technique is statistically based.

[0010] Still another property of a proper watermarking technique is thatit should be possible to vary the degree of marking applied to an image.In this way, the watermark can be made as detectable as necessary by theparticular application. This property is important in highly texturedimages where it is often necessary to increase the intensity of the markto increase its likelihood of detection. This is in contradistinctionwith images that have low contrast in which it is advantageous to reducethe marking intensity to lessen undesirable visible artifacts of thewatermark itself.

[0011] It is also highly desirable that when detected the demonstratedexistence of the watermark should be translatable to a recognizablevisual image having relatively bold features with a high contrast ratio.Features of a demonstrated visual image that are not relatively bold mayotherwise be difficult to show if the watermark has been attacked inattempts to defeat its protection.

[0012] Finally, the imparted watermark should be robust in that itshould be very difficult to be removed or rendered undetectable. Itshould survive such image manipulations that in themselves do not damagethe image beyond usability. This includes, but is not limited to, JPEG“lossy” compression, image rotation, linear or nonlinear resizing,brightening, sharpening, “despeckling,” pixel editing, and thesuperposition of a correlated or uncorrelated noise field upon theimage. Attempts to defeat or remove the watermark should be generallymore laborious and costly than purchasing rights to use the image. Ifthe image is of rare value, it is desirable that the watermark be sodifficult to remove that telltale traces of it can almost always berecovered.

SUMMARY OF THE INVENTION

[0013] An aspect of the present invention is to provide a method forimparting a watermark onto a digitized image comprising the steps ofproviding the digitized image, and multiplying the brightness dataassociated with at least one of the image pixels by a predeterminedbrightness multiplying factor. The image includes a plurality of pixels,wherein each of the pixels includes brightness data that represents onebrightness value if the image is monochrome, or a plurality ofbrightness data values if the image has multiple colors. A brightnessdata value of a pixel and a color component or component are hereinafterused to mean the same thing, and are therefore to be consideredinterchangeable. In an embodiment, the brightness multiplying factorranges from 0.5 to 1.0. Other smaller or larger factors are useful insome image applications dependent upon particular desired watermarkingresults. The brightness multiplying factor has a relationship with anumber taken from a random number sequence and the relationship is alinear remapping to provide a desired modulation strength.

[0014] In an embodiment, each of the pixels has a row and a columnlocation in an array representing the digitized image, and thebrightness multiplying factor employs a different sequential combinationof numbers from a robust random number sequence in sequentialcorrespondence to the row and column location.

[0015] Another aspect of the present invention is to provide a methodfor generating a watermarked image wherein a watermark is imparted ontoa digitized image having a plurality of original pixels, each pixelhaving original brightness values. The method includes the step ofproviding a digitized watermarking plane comprising a plurality ofwatermarking elements, each having a brightness multiplying factor andhaving one-to-one positional correspondence with the original pixels. Italso includes the step of producing a watermarked image by multiplyingthe original brightness values of each of the original pixels by thebrightness multiplying factor of a corresponding one of the watermarkingelements wherein the watermark is invisible. In an embodiment, when theoriginal image forms an original plane and the watermarking plane issmaller than the original plane, the method further includes the step ofextending the watermarking plane by tiling such that the watermarkingplane covers the original plane and/or further comprises the step oftruncating the watermarking plane such that the watermarking planecovers the original plane, upon determining that the watermarking planeextends beyond the original plane.

[0016] Another aspect of the present invention is to provide a methodfor forming a watermarking plane including a plurality of elements eachhaving a multiplying value. The method comprises the steps of:generating a robust random sequence of integers having a first pluralityof bits; linearly remapping the random sequence to form a remappedsequence of brightness multiplying factors to provide a desiredmodulation strength; computing a discrete Fourier transform of theremapped sequence to form a Fourier sequence having frequencycoordinates; expanding the frequency coordinates to form an expandedsequence; and computing an inverse Fourier transform of the expandedsequence to obtain a watermarking sequence of values.

[0017] An embodiment further includes one or more or the following: thestep of expanding is accomplished by zero-padding; the method furthercomprises a step of employing the watermarking sequence to provide themultiplying value for each of the elements; the method further comprisesthe steps of hard clipping the watermarking sequence to form ahard-clipped sequence having sequence members, and utilizing a differentone of the sequence members to provide the multiplying value for each ofthe elements; the method further comprises the steps of adjusting thewatermarking sequence to form a normalized sequence of values having amean and a median equal to the difference between unity and themodulation strength, and having a maximum of unity, and employing thenormalized sequence to provide the multiplying value for each of theelements; the method further comprises the steps of providing anunmarked original image having a plurality of original pixels, each ofthe pixels having at least one component, wherein a first number of theoriginal pixels is greater than a second number of the plurality ofelements, expanding the watermarking plane by tiling to cover theunmarked original image such that one of each of the pixels has onecorresponding element from the elements; and multiplying the at leastone component of each of the pixels by the multiplying value of thecorresponding element.

[0018] Still another aspect of the present invention is to provide amethod for detecting a watermark in a marked image. The marked image ismarked by a watermarking plane which has a plurality of watermarkingelements. Each of the image pixels has at least one component and eachof the watermarking elements has a brightness multiplying factor. Themethod employs a selector having at least one element and a visualizerhaving at least one pixel and at least one counter, said at least onecounter to store the comparison data resulting from comparisons for eachof a plurality of selector elements and positions; said comparison dataresulting from the comparison of the statistical brightness of eachimage color component, relative to its neighboring color components inthe same plane, with the statistical magnitude of each correspondingbrightness multiplying factor, relative to its neighboring multiplyingfactors. The method further comprises the step of displaying avisualizer-coincidence image such that a user can make a determinationas to whether the pattern encoded by the visualizer pixels isrecognizable and thereby, whether the watermark is detected.

[0019] Further, it is an aspect of the present invention to provide analternative method and apparatus for imparting a watermark into adigitized image that includes the step of providing the digitized imageand the step of adding at least one predetermined brightness adjustingvalue to the brightness data associated with at least one of the imagepixels. The image includes a plurality of pixels, wherein each of thepixels includes brightness data that represents one component if theimage is monochrome, or a plurality of components if the image hasmultiple colors. The step of “adding a predetermined brightness datavalue to a component” is used in the same way as the step of“multiplying a component by a predetermined brightness multiplyingfactor”, where the component is associated with at least one of theimage pixels. Under conditions that will be specified, the step ofadding achieves image watermarking results which are similar in everymanner and respect to the step of multiplying. The additive brightnessadjusting values may be positive or negative, and a color componentaltered by the step of adding increase or decrease accordingly.

[0020] In another aspect of a general embodiment, the components of allimage pixels, or all image pixels in a specified image portion, are eachmodified by an associated brightness adjusting factor.

[0021] In another particular embodiment, each of the pixels has a rowand a column location in an array representing the digitized image, andthe brightness adjusting factors for each pixel employ a differentsequential combination of numbers from a different robust random numbersequence in sequential correspondence to the row and column location.

[0022] Another aspect of the present invention is to provide a methodfor generating a watermarked image wherein watermarks are imparted intoa digitized image by having a plurality of original watermarkingelements, with each of the elements having an original brightnessadjusting value.

[0023] Another aspect of the present invention is to provide a methodfor forming watermarking planes. Each watermarking plane includes aplurality of elements with at least one brightness adjusting valuederived from each element.

[0024] Still another aspect of the present invention is to provide amethod for improving the probability of detection of a watermark in amarked image or a derived copy of a marked image. The marked image ismarked by a watermarking plane which has a plurality of watermarkingelements. The method applies a two-dimensional blurring filter to themarked image or derived copy of a marked image prior to attempteddetection of the imparted watermark.

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] These and other objects, features, and advantages of the presentinvention will become apparent upon further consideration of thefollowing detailed description of the invention when read in conjunctionwith the drawing figures, in which:

[0026]FIG. 1 shows a block diagram of an image capture and distributionsystem suitable for use in accordance with an embodiment of the presentinvention.

[0027]FIG. 2 shows an embodiment for forming a watermarking plane inaccordance with the present invention.

[0028]FIG. 3 shows an embodiment for the steps of watermark imparting.

[0029]FIG. 4 shows an overview of the steps for image alignment.

[0030]FIG. 5 shows the steps for a coarse alignment of a marked imagewith a correlation reference plane.

[0031]FIG. 6 shows the steps for a fine alignment of a marked image witha correlation reference plane.

[0032]FIG. 7 shows the steps for finding a watermark in a marked image.

[0033]FIG. 8 shows a random positioning of the selector array over thewatermarking plane and the image planes.

[0034]FIG. 9 shows a typical visualizer pattern.

[0035]FIG. 10 shows a method of verification of the presence of thewatermark.

[0036]FIG. 11 shows a detection resulting from the visualizer of FIG. 9for a watermarking made at a modulation strength of 1%.

[0037]FIG. 12 shows a detection resulting from the visualizer of FIG. 9for a watermarking made at a modulation strength of 2%.

[0038]FIG. 13 shows a detection resulting from the visualizer of FIG. 9for a watermarking made at a modulation strength of 4%.

[0039]FIG. 14 shows a detection resulting when the image has nowatermark.

[0040]FIG. 15 shows the steps for an alternate method of finding awatermark in a marked image.

[0041]FIG. 16 shows an enlarged segment of a watermarked image, havingbeen watermarked at a modulation strength of 2.5%, that is used as thereference image.

[0042]FIG. 17 shows the enlarged segment of the reference image after ithas been prepared for printing by screening, has been printed and hasbeen scanned to form the derivative image.

[0043]FIG. 18 shows the enlarged segment of the derivative image thathas been acted upon by a blurring filter to form the filtered image.

[0044]FIG. 19 shows a visualizer-coincidence image resulting from awatermark detection made on the reference image.

[0045]FIG. 20 shows a visualizer-coincidence image resulting from awatermark detection made on the derivative image.

[0046]FIG. 21 shows a visualizer-coincidence image resulting from awatermark detection made on the filtered image.

DETAILED DESCRIPTION OF THE INVENTION

[0047] The present invention provides a robust means of watermarking adigitized image with a highly random sequence of pixel brightnessmultipliers. The random sequence is formed from four‘robust-watermarking-parameters’ selected and known only by the markerand/or the marking entity. A watermarking plane is generated which hasan element array with one-to-one element correspondence to the colorcomponent array or arrays of the digitized image being marked. Eachelement of the watermarking plane is assigned a random value dependentupon a robust random sequence and a specified brightness modulationstrength. The so generated watermarking plane is imparted onto thedigitized image by multiplying the brightness value or values of eachpixel by its corresponding element value in the watermarking plane. Theresulting modified brightness values impart the random and relativelyinvisible watermark onto the digitized image. Detection of an impartedwatermark requires knowing the watermarking plane with which thewatermark was imparted. Regeneration of the watermarking plane requiresknowledge of the robust-marking-parameters used in its formulation. Thisis generally only known to the marker and/or marking entity. Onceregenerated the watermarking plane is used together with a verifyingimage located in a ‘visualizer’ to demonstrate the existence of thewatermark.

[0048] Brightness modulation is the essence of watermark impartingaccording to the present invention. Pixel brightness, as used herein,expresses the brightness of a visual stimulus in terms of the CIE 1931Standard Colorimetric Observer and Coordinate System tristimuluscomponent brightness X, Y and Z that correspond to a matching mixture ofthree reference stimuli. If the image is monochrome, pixel brightnessexpresses the brightness of a visual stimulus in terms of the CIE 1931Standard Coordinate System photopic brightness Y, and components X and Zhave no meaning. A more detailed description of pixel brightness isfound in G. Wyszecki and W. S. Styles, “Color Science: Concepts andMethods, Quantitative Data and Formulae,” John Wiley & Sons, Inc. (2nded.), New York, 1982, pp. 164-169, incorporated herein by reference inits entirety. The CIE 1931 standard specifies three particular referencestimuli. The stimuli are radiometric quantities, and as such areexpressed in radiometric units such as watts. Grassmann's law, on whichnearly all of modern colorimetry is based, requires use of the threespecific reference stimuli, or three others that are distinct linearcombinations of them. This is discussed in D. B. Judd and G. Wyszecki,“Color in Business, Science, and Industry,” (3rd ed.), John Wiley &Sons, Inc., New York, 1975, pp. 45-47, incorporated herein by referencein its entirety. By modifying only a pixel's brightness, its color,represented by its hue and saturation, is not changed. This isaccomplished by preserving the ratios of X:Y and Z:Y while changing themagnitude of Y. A pixel represented in any nonlinear color space, suchas the color space of the subtractive dyes Cyan, Magenta, Yellow andBlack (CMYK) used in color printing, will be translated to the X, Y, Zcolor space (or to a color space linearly related to it) before thepixel's brightness is modified.

[0049]FIG. 1 shows a block diagram of a system embodiment for impartinga relatively invisible watermark on a digitized image in accordance withthe present invention. FIG. 1 shows an image capture and distributionsystem 150 suitable for use in accordance with an embodiment of thepresent invention. A scanner 100 captures image data 101 from a physicalsource 102. The physical source 102 is typically a painting orphotograph. The image sends data 101 to a digital computer 104. Thecomputer 104 includes a working storage 106 that is typically embodiedin the computer's random access memory, an image storage system 108 thatis often a conventional hard disk drive, and an image archive 110 thatcan be a tape or disk storage. The computer 104 also includes a numberof software modules. These include front end image processing software112 that performs image processing such as scaling and enhancement ofthe image data provided by the scanner 100. It also includes colorpreserving watermarking software 114 operating in accordance with theprinciples of the present invention, and back-end image processingsoftware 116 that performs other processing functions such ascompression on the watermarked image. Most often, the unprocessed orfront-end digitized original image 101 is sent to the image archive 110for preservation in unwatermarked form.

[0050] An alternate embodiment has the original image already availablein digitized form 101 without requiring a scanner 100. The watermarkingsoftware 114 applies a relatively invisible watermark to the digitizedimage 101 in accordance with the principles of the present invention.The watermarking process can also be performed on a copy of an archivedimage or on other scanned and processed image data, which has beenloaded in whole or in part, into the computer's working storage 106.

[0051] The processed, watermarked and compressed image produced by thecombination of the software modules 112-116 is sent from the workingstorage 106 or image storage 108 to an image server 118 that isconnected to a digital network 120. When appropriate, the digitalnetwork is interconnected with a Local Area Network (LAN), a Wide AreaNetwork (WAN) such as the Internet, or both. Other systems 122 connectedto the digital network 120 can request and receive images stored on theimage server 118 via the digital network 120. In some cases, the systemscan then display the received images on a display device 124 and/orprint the images on a graphics capable printer 126. Those skilled in theart will recognize that there are many other system configurations inwhich the present invention could be employed. The system of FIG. 1 isgenerally also useful for detecting and demonstrating the existence ofthe watermark in a manner such as those described subsequently.

[0052] Marking an Image with a Robust Watermark

[0053] In one embodiment, the watermark imparted onto the digitizedimage is a monochrome pattern, herein called “the watermarking plane,”that overlays the digitized image. The pattern is embodied by selectingits element values from a robust random sequence formed from a group ofrobust sequence generating parameters. The parameters are used togenerate a generally strongly encrypted random sequence in a manner wellknown to those skilled in the art. These parameters are herein referredto as the ‘robust-watermarking-parameters’. In a preferred embodiment,these parameters include a cryptographic key, two coefficients of alinear random number generator, and an initial value of the randomnumber generator.

[0054] Each value, or group of values, of the robust random sequence isassociated with one of the pixels of the digitized image. Most often thevalues of the random sequence are linearly remapped to meet particularcriteria. All the brightness values of the plurality of color planes ofeach pixel are multiplied by its associated linearly remapped robustrandom sequence value called its brightness multiplying factor ormultiplying factor. A brightness multiplying factor which modifies pixelbrightness values by less than ten percent is herein referred to as abrightness multiplying factor producing a relatively invisiblewatermark. It is noted that depending on the texture of the image beingwatermarked, the brightness values are generally modified on average bya percentage factor of only 0.3 to 4 percent, and rarely up to 10percent. This is in order to make the marking less visible. Thepercentage factor is herein referred to as the modulation strength. Theactual modulation strength employed is dependent upon the classificationlevel of invisibility required by the particular use. It is notadvisable to employ a brightness multiplying factor greater than unity.This can result in some pixel brightness values being greater than one.If employed, it is recommended that all brightness values greater thanone be clipped to a value of unity. This can alter the pixel's color,thus altering the appearance of the image.

[0055] Imparting a watermark upon a digitized image by varying thebrightness of each pixel with a multiplying factor maintains eachpixel's color by satisfying Grassmann's law. A compromise is generallymade in selecting modulation strength. A smaller percentage makes thewatermark less visible but more difficult to detect. A larger percentagemakes it easier to detect and demonstrate the existence of thewatermark, but makes the watermark more visible. A highly textured imagemay require the use of a relatively high modulation strength. Animparted watermark is considered to be undetectably invisible in allcases if the modulation strength is less than 0.5 percent, even when theunmarked digitized image is a uniform medium gray. For digitized imageshaving more practical and valuable features, subliminally invisiblewatermarks generally have modulation strengths of 1% to 3%, depending onthe degree of textural variation in the image itself.

[0056] The watermark imparted in accordance with this invention isselected so as to appear to be relatively invisible to any person havingnormal or corrected visual accommodation. The probability of afalse-positive detection of the watermark in an image when it does notexist is less than one in a million. It is possible to vary the degreeof imparted watermarking onto the image so that the watermark can bemade as detectable as necessary consistent with a required invisibilityclassification. The detected watermark is translatable to a recognizablevisual image, called a visualizer, having relatively bold features andwith a very high contrast ratio. The watermark once imparted, is verydifficult to remove or to be rendered undetectable without reducing theusefulness and/or value of the digitized image.

[0057] In an embodiment of this invention, marking a digitized imagewith an invisible watermark requires the formation of a plane forwatermarking. The invisible watermark is herein represented as arectangular array of numeric elements, henceforth referred to as thewatermarking plane, having I rows and J columns. The I rows and Jcolumns correspond to the dimensions of the entire original digitizedimage, or a portion thereof, to which it is being applied.

[0058] When an original digitized image is very large, a generatedwatermarking plane not large enough to cover the entire original imageis extended by tiling replication in any direction necessary to coverthe entire image. If a watermarking plane being so tiled extends beyondany edge of the original image, the watermarking plane is assumed to betruncated. These conventions are adopted for this embodiment to allowevery pixel of the original image to have its brightness altered and toensure that the marked image is equal in size to the original image.This forms a one-to-one correspondence between element locations in thewatermarking plane and color components in the color planes of theoriginal image. This is generally a desirable implementation, eventhough alternate embodiments do not require watermarking the entireimage.

[0059] In a preferred embodiment, the value of each element in the arraydefining the watermarking plane is linearly remapped to be a randomnumber in the range,

1≧w(i, j)≧(1−2β),  (1)

[0060] where,

1≦i≦I,  (2)

[0061] and

1≦j≦J,  (3)

[0062] are the row and column indices of the array, and β is themodulation strength of the watermark such that,

0.5≧β≧0.  (4)

[0063] Additionally, all elements in the generated watermarking plane,treated as an ensemble, are adjusted to have a mean and median of 1−β.

[0064] Imparting the watermark onto an image begins with generation ofthis watermarking plane. The watermark is imparted onto the originalimage by multiplying all the brightness values associated with everypixel in each color plane by the value in its corresponding element inthe watermarking plane.

[0065] Constructing the Watermarking Plane

[0066] The construction of the watermarking plane is fundamental toinsuring the robustness of the imparted watermark and its ability tosurvive even determined attacks. To this end, the procedure by which thevalues of the watermarking plane elements are chosen is based oncryptographic and two-dimensional signal processing theory techniques.These are used to satisfy particular requisite properties of thewatermarking plane.

[0067] The Property of Unpredictable Randomness

[0068] Consideration is now given to the values of the watermarkingplane elements to meet the property of unpredictable randomness.Unpredictable randomness requires that each element's value should varyrandomly from the values of its neighbors, and the sequence of elementvalues should be essentially unpredictable. Random variation of theelements is required for the watermark to be rendered relativelyinvisible. In as much as pattern recognition is one of the most dominantcharacteristics of the human visual system, the presence of any patternamong elements of the watermarking plane could make it visible. Theunpredictability of the sequence of values is required to make thewatermark robust and less vulnerable to attack. It is recognized that ifall values in the watermarking plane could be predicted, thewatermarking process could easily be reversed and the mark removed. Thiscould thereby be used to essentially restore the marked image to anearly perfect copy of the original unmarked image. Thus, a means ofgenerating a highly unpredictable random number sequence is preferred.

[0069] Generating random values by a congruence method, typical ofnearly all popular pseudo-random number generating algorithms, is notconsidered herein to provide an adequate level of unpredictability.These sequences have only modest cryptographic strength and arerelatively easily discernible by crypto-analytic techniques. This isdescribed in “The Cryptographic Security of Truncated Linearly RelatedVariables,” J. Hastad and A. Shamir, Proceedings of the 17th Annual ACMSymposium on the Theory of Computing, 1985, pp 356-.362, which is hereinincorporated by reference.

[0070] For the purposes of this invention a sequence is generated byusing a strong cryptographic method such as the National Standard DataEncryption Algorithm. This is described in: “American National StandardData Encryption Algorithm,” ANSI X3.92-.1981, American NationalStandards Institute, New York; and in A. G. Konheim, et al., “The IPSCryptographic Programs,” IBM System Journal, Vol. 19, No. 2, 1980, pp253-283; which are herein incorporated by reference.

[0071] The data sequence of eight-bit values to be encrypted is selectedby the marker, and is desirably generated by a congruence algorithm.However, the robust secure sequence is produced by action of the strongencryption algorithm on that data. Using this approach, a highlyunpredictable watermarking plane can be produced. Moreover, it can bereproduced exactly by knowing only its four‘robust-watermarking-parameters’. These parameters are the initial stateand the two coefficients of the congruence algorithm, and thecryptographic key used by the encryption algorithm. These algorithmsgenerally produce sequences of values having eight-bits. Sixteen-bitvalues, referred to as α(i, j), are generated by concatenating two ofthe sequential eight-bit values produced by the encryption algorithm.Each sixteen-bit value so produced is linearly remapped to become anelement of the array defining the watermarking plane as follows:

w(i, j)=1−2β[1−α(i, j)/65535]  (5)

[0072] Additionally, all elements in the w(i, j) array, treated as anensemble, are adjusted to have both a mean and median of 1−β. Ease ofreproduction of the resulting encrypted sequence is important forwatermark detection and demonstration techniques discussed subsequently.Other remapping or normalization techniques producing particular desiredresults are known to those familiar with the art.

[0073] The Property of Explicit Low Frequency Content

[0074] Another important consideration is for an embodiment thatexploits the property of explicit low frequency content. Significanthigh frequency content results when the watermarking plane is composedby placing a unique random value in every element. Although highfrequency content is beneficial in making the watermark less visible, italso makes it vulnerable to attack for watermark damage or extinction.This is evident from the following consideration. The highest patternfrequency achievable in a digitized image is obtained by replicating apair of adjacent pixels that have opposite extreme values. When theimage is reduced in size, if image reduction filtering is used, thevalues of adjacent pixels are combined in a weighted average to formpixel values of the reduced image. If image decimation is used, pixelsare selectively discarded. In either event, the high frequency contentin the original image is lost in the reduced image. Any significant highfrequency content in the applied watermarking plane becomes obliteratedin the reduced image. Subsequent detection of the watermark impartedprior to the size reduction is very difficult if not impossible. Thepurposeful addition of low frequency content makes the watermark lessvulnerable to this type of attack. However, the deliberate inclusion ofsignificant low frequency content in the watermarking plane is anotherdichotomy. Its inclusion indeed makes the watermark less vulnerable tonormal image manipulation and therefore more easily detectable. However,it generally makes the watermark more visible by producing a patternwith larger features in the watermarking plane. It is generallypreferable to add only a controlled amount of low frequency content.

[0075] The deliberate addition of low frequency content to the originalwatermarking plane is accomplished in one embodiment by employing thetwo-dimensional discrete Fourier transform. First, a reduced-sizewatermarking plane is formed whose elements are uniformly distributedrandom values in accordance with the secure sequence described above.For discussion purposes, a square plane w(μ, ν) having 0≦μ≦Λ−1 rows and0≦ν≦Λ−1 columns is used. The discrete Fourier transform of the squareplane is computed. Since all values of w(μ, ν) are real numbers,advantage can be taken from the complex-conjugate symmetry of itsFourier transform. The complete Fourier transform can be specified asthe array of complex numbers W(σ, τ) having dimensions 0≦σ≦Λ−1 and0≦τ≦Λ/2, and is symbolized as:

W(σ, τ)=F[w(σ, τ)]  (6)

[0076] The frequency domain array W(σ, τ) is remapped into an expandedarray W(s, t), where:

0≦s≦L−1, 0≦t≦L/2, and L=2^(ρ)Λ,

[0077] thus enlarging the (σ, τ)-space by the factor 2^(ρ) in eachdimension forming the larger (s, t)-space. If W(σ, τ) is defined suchthat W(0, 0) is the coefficient of the constant or “zero-frequency”term, then:

W(L−s, t)=W(Λ−σ, τ),  (7)

[0078] and

W(s, t)=W(σ, τ),  (8)

[0079] for

0≦s=σ<Λ/2 and 0≦t=t≦Λ/2,  (9)

[0080] and

W(s, t)=0  (10)

[0081] for all other values of s and t. This technique is hereinreferred to as “zero-padding.”

[0082] The inverse Fourier transform of W(s, t) provides the modifiedwatermarking plane w(m, n) having 0≦m≦L−1 rows and 0≦n≦L−1 columns. If,for example, ρ=2 and Λ=512, then w(m, n) is a square array having 2048rows and columns. More importantly, however, w(m, n) has an assured lowfrequency content with a minimum period (2^(ρ)=2²=4) four times longerthan the minimum period possible in a 2048² image plane. Since itsgenerating kernel, w(μ, ν), contains 262,144 random values taken from asecure sequence, its vulnerability to attack by brute force replicationis relatively small. In a case where a thus marked image appears to bevulnerable, its kernel can easily be made larger. Still lower frequencycontent can be impressed by using a ρ=3, making the highest frequency tobe one eighth of the original highest frequency. The preferredembodiment uses ρ=2 so as not to over employ low frequency content thatmay cause the watermark to become undesirably visible.

[0083] The values of some elements of the generated watermarking planeso far produced may exceed one. Since each value is to be used as amultiplier of pixel brightness, it is therefore possible to produce amultiplied pixel brightness that is greater than one [i.e. greater thana maximum brightness], which is a brightness that can not physically bedisplayed. In this event, any multiplied pixel brightness greater thanone would have to be clipped to the maximum that can be displayed. Thepreferred embodiment, however, employs an additional process step toavoid the possible need for clipping. Before the generated modifiedwatermarking plane is used, its elements, forming an ensemble, areadjusted to make both their mean and median values equal to 1−β and themaximum value equal to 1. With these adjustments, the requirement that,

1≧w(i, j)≧(1−2β),  (11)

[0084] for all i and j is satisfied.

[0085] At this point, it is sometimes advantageous to “hard clip” theelements. In this situation, elements with values greater than or equalto 1−β are set to 1, and elements with values less than 1−β are set to1−2β. Hard clipping normally increases the probability of detecting awatermark, but unfortunately, it also tends to make watermarkingartifacts more visible in the marked image.

[0086] The Property of Plane Expansion by Tiling

[0087] The fact that the watermarking plane w(m, n) is produced as theresult of an inverse discrete Fourier transform is very useful. If thewatermarking plane is not large enough to cover the entire unmarkedimage, if L<I or L<J, it can be enlarged seamlessly by tilingreplication downward or to the right to make a plane as large asdesired, with each tiled extension adding an additional 4,194,304elements. For the example dimensions used here, tiling replication is:

w(m′, n′)=w(m, n),  (12)

[0088] where,

m′=(2048p)+m,  (13)

n′=(2048q)+n,  (14)

[0089] and p and q are non negative integers.

[0090] In one embodiment, a watermarking plane is formed following thesteps 202-216 shown in FIG. 2. These steps are herein referred to as the‘ideal interpolator watermarking plane generating method’. Firstly, aneight-bit pseudo-random sequence is generated, 202. The resultingsequence is encrypted to form a secure sequence of eight-bits values,204. Sixteen bit integer samples are formed by concatenating two abuttedvalues from the secure sequence, 206. The sixteen bit integer samplesare linearly remapped and formed into a w(μ, ν) array such that,

1≧w(μ, ν)≧(1−2β),  (15)

[0091]208. The discrete Fourier transform frequency domain array W(σ, τ)is computed from w(μ, ν), 210. The W(σ, τ) coordinates are expanded byzero-padding to form expanded frequency domain array W(s, t), 212. Thepreliminary watermarking plane array w(m, n) is computed by taking theinverse discrete Fourier transform of W(s, t), 214. The elements of thepreliminary array w(m, n) are adjusted to collectively have a mean andmedian of (1−β) and a maximum of 1, 216 a. Alternatively, the elementsw(m, n) are hard clipped to have only values of 1 or 1-2β, with a medianof 1−β, 216 b. The resulting adjusted array w(m, n) is the watermarkingplane with elements that are brightness multiplying factors to be usedfor adjusting corresponding pixels of the image being watermarked.

[0092] The method presented here, employing forward and inverse discreteFourier transforms to generate the watermarking plane, is an “idealinterpolator” with assured low frequency content. Other methods known tothose skilled in-the-art are available. These include methods that usetwo-dimensional interpolation filters that can similarly be employed toproduce acceptable results.

[0093] The generated watermarking plane is then imparted onto theoriginal unmarked digitized image. FIG. 3 shows an embodiment for thesteps of watermark imparting. First, the watermarking plane is expandedby tiling to completely cover the image being watermarked, 302. Thisforms a one-to-one correspondence of an element in the expandedwatermarking plane and a pixel in the original image. The brightnessvalues of each pixel in the original image are multiplied by the valuein its corresponding element in the expanded watermarking plane, 304.The resulting image with the new brightness values forms the watermarkedimage. The relative visibility of the watermark in the image is observedin relationship to the desired visibility classification level marking.If the marking is more visible than specified the steps of FIGS. 2 and 3are repeated for a lower modulation strength. A watermark created with alower modulation strength is generally less easily detected anddemonstrated to exist. One the other hand, if the resulting watermark isless visible than specified, the steps of FIGS. 2 and 3 may be repeatedto provide a watermark with a higher modulation strength. A watermarkcreated at a higher modulation strength is generally easier to detectand have its existence demonstrated. Once imparted, an invisiblewatermark only serves its purpose if it can be detected and shown toexist.

[0094] Finding an Invisible Watermark Hidden in a Marked Image

[0095] It is most desirable to demonstrate the existence of thewatermark with a visible image having bold features. This is hereinemployed using an image array called a “visualizer.” Demonstration ofthe existence of the watermark imparted in accordance with the-presentinvention requires a regeneration of the watermarking plane with whichit was marked. This can generally only be performed by the marker and/ormarking entity who alone knows the four parameters making up thisapplication's “robust-watermarking-parameters”′. Knowledge of theseparameters is required for generating the robust random sequence used informing the watermarking plane. From these four parameters the robustrandom sequence is reformed. Values of the sequence are used to definethe values of the elements. If a linear remapping process was employedin the generation of the watermarking plane, the element values arelinearly remapped using that same process to redefine the expandedwatermarking plane. The thus reformed expanded watermarking plane isused in conjunction with the visualizer to demonstrate the existence ofthe expanded watermarking plane in the image. This is accomplished asdescribed subsequent to an overview of watermark detectionconsiderations.

[0096] Finding an invisible watermark hidden in a marked digitized imageis a relatively difficult problem, and it is made more so bymanipulations of the marked image that may have occurred. The watermarksurvives and is detectable for image manipulations that in themselves donot damage the image beyond usability. The detection method of thepresent invention can find an imparted watermark with a high degree ofcertainty in nearly all such cases. A significant advantage of thepresent method is that watermark detection does not require access to acopy of the entire original image. In most cases, all that is requiredis the watermarking plane used for imparting the watermark on the image.A perfect copy of the watermarking plane is reconstituted from its fourdefining parameters. If a copy or if even only a fragment of theoriginal image is available, detection can have a somewhat higherprobability of success.

[0097] Reorienting and Resizing the Watermarking Plane

[0098] A first consideration in finding a watermark is to determine howand by how much the marked image may have been manipulated. It may havebeen reduced in size. A size reduction may even have been performednonlinearly, such that its horizontal and vertical dimensions may havebeen reduced by unequal factors. The image may also have been rotated,not by an obvious ninety degrees, but by a small angle. Facilitatingthis determination is the knowledge that pixel values in theunmanipulated marked image are directly related to correspondingelements in the watermarking plane. If a significant fragment of theoriginal image is available, a fragment of the unmanipulated markedimage can be reconstructed. Either the reconstituted watermarking planeor a reconstructed fragment of the marked image is a suitable“correlation reference plane.”

[0099] An overview of the steps of reconstructing a manipulatedwatermarked image is shown in FIG. 4. First, the watermarking plane usedfor imparting the watermark onto the image is regenerated from the four‘robust-watermarking-parameters’ generally only known to the markerand/or the marking entity, 402. Secondly, the marked image is resizedand rotated to its known original dimensions, 404. Thirdly, the resizedand rotated image is aligned with the expanded regenerated watermarkingplane such as to provide one-to-one correspondence of the elements ofeach with the elements of the other, 406.

[0100] In an actual implementation the steps of reorienting and resizingthe marked image may be broken into a coarse placement followed by afine alignment. The coarse placement is performed by visual inspectionof a displayed copy of a portion or the complete marked image overlayinga corresponding portion or complete correlation reference plane. Thecorrelation reference plane is reoriented and resized to the size andorientation of the marked image by axis reduction or expansion,translation and/or rotation. This is accomplished using techniques wellknown to those skilled in the art. The coarse placement generally bringsthe correlation reference plane to within 4 percent of the manipulatedmarked image's size and within four degrees of its orientation.

[0101]FIG. 5 shows the steps for an embodiment for performing coarseplacement. Both the marked image and the correlation reference plane aredisplayed on a common display, 502. The vertical axis and horizontalaxis magnification, offset and angular rotation of the correlationreference plane display are varied to make the displayed correlationreference plane closely overlay the corresponding portions of thedisplayed manipulated marked image, 504. The values of themagnification/reduction factors, horizontal and vertical offsets andangle of rotation are noted and stored, 506. The entire marked image isrescaled, translated and rotated by the inverses of the noted values sothat it visually matches the correlation reference plane, 508. The socoarsely manipulated reconstituted marked image is further manipulatedto perform the fine alignment.

[0102] According to the Fourier Shift Theorem, Rotation Theorem andScaling Theorem, the properties of translation, rotation and scalingtranscend the Fourier transformation of an image, and, if present inw(m, n), each will also be present (or, in the case of scaling, itsreciprocal will be present) in W(s, t). This is useful to determine amore precise angle of rotation, horizontal and vertical scale factors,and translation offsets of the correlation reference plane relative tothe marked image. This is accomplished by first constructing athree-dimensional “array of phase-correlation maxima.” The three axes ofthe array correspond to the horizontal scale factor, the vertical scalefactor, and the angle of rotation of the correlation reference planerelative to the marked image. Phase-correlation is defined as follows.Let W(s, t) be the discrete Fourier transform of the correlationreference plane, U(s, t) be the discrete Fourier transform of the markedimage u(m, n), and U*(s, t) be the complex conjugate of U(s, t). Thephase-correlation plane p(m, n) is computed using the relationship:$\begin{matrix}{{p\left( {m,n} \right)} = {{F^{- 1}\left\lbrack \frac{{W\left( {s,t} \right)}U*\left( {s,t} \right)}{\left| {{W\left( {s,t} \right)}U*\left( {s,t} \right)} \right|} \right\rbrack}.}} & (16)\end{matrix}$

[0103] The value at each array point is the maximum magnitude of thecorresponding phase-correlation plane. It is computed using anincrementally rescaled and rotated correlation reference plane. Any oneof the color planes of the marked image usually suffices as the requiredarray u(m, n). Interpolating among the values of the three-dimensionalarray yields coordinates of the greatest-of-the-greatestphase-correlation maxima. From these coordinates, values of thehorizontal and vertical scale factors and angle of rotation of thecorrelation reference plane relative to the marked image are directlyread. The correlation reference plane is then rescaled and rotated tomore precisely align it with the manipulated marked image. A finalphase-correlation evaluation is made to determine the relativehorizontal and vertical offsets of the modified correlation referenceplane relative to the manipulated marked image. Finally, the entiremarked image is rescaled, translated and rotated in accordance with theinverses of the measured values to restore it to its original size andorientation. The thus modified marked image is now ready for use in thedetection and demonstration process to show the existence of thewatermark in the manipulated marked image.

[0104] In one embodiment the fine alignment of the correlation referenceplane relative to the marked image is performed by evaluating athree-dimensional array of phase-correlation maxima, and theninterpolating within that array to find the location of the maximum ofthose maxima. The axes of the array are the horizontal magnification,vertical magnification and angular rotation that are systematicallyapplied to the correlation reference plane. All combinations of thefollowing incremental steps define the values of the coordinates of thearray. The vertical axis of w(m, n) is magnified/reduced from 96% to104% of its original size in 2% increments. In similar fashion thehorizontal axis of w(m, n) is magnified/reduced from 96% to 104% of itsoriginal size in 2% increments. Also in similar fashion w(m, n) isrotated relative to its original orientation from −5 degrees to +5degrees in 2 degree steps. At each combination of verticalmagnification, horizontal magnification, and angular rotation of thecorrelation reference plane, the phase-correlation plane p(m, n) isrecomputed as above. The maximum of the point values p(m*, n*) in theplane is stored into the three-dimensional array of phase-correlationmaxima at coordinates corresponding to each of the incrementallyadjusted values of vertical magnification, horizontal magnification, andangular rotation.

[0105] A flow diagram of this embodiment is shown in FIG. 6. Thoseskilled in the art know there are many satisfactory algorithms availableto magnify/reduce and rotate digitized images. Any one of thosealgorithms can be used for manipulation of the correlation referenceplane in the following description. As described above, the discreteFourier transform of the marked image U(s, t) is formed, 602. Initialvalues are set for stepping variables vertical magnification, Vm=0.96,horizontal magnification, Hm=0.96, and angular rotation, Ar=−5°, 604.The correlation reference plane is vertically magnified/reducedaccording to Vm, 606. The so adjusted plane is then horizontallymagnified/reduced according to Hm, 608. The so adjusted plane is thenrotated according to Ar, 609. The discrete Fourier transform of the soadjusted plane W(s, t) is formed, 610. The phase-correlation plane p(m,n) is calculated using the relationship of equation (16), 611. The p(m,n) plane is examined to find the coordinates (m*, n*) of its maximumvalue, 612. The coordinates (m*, n*) and p(m*, n*) are stored in thethree-dimensional array being formed. The three-dimensional array isindexed by Vm, Hm and Ar, 613. The value of Ar is examined, 614. If itis less than plus five degrees, it is incremented by plus two degrees,615, and steps 609-614 are repeated until Ar is found to be plus fivedegrees in step 614. When Ar is found to be plus five degrees in step614, the value of Hm is examined, 616. If Hm is less than 1.04, it isincremented by 0.02 and Ar is reinitialized to minus five degrees, 617.Steps 608 to 616 are repeated until Hm is found to be 1.04 in step 616.When Hm is found to be 1.04, Vm is examined, 618. If Vm is found to beless than 1.04, it is incremented by 0.02, and Ar is initialized tominus five degrees, and Hm is initialized to 0.96, 619. Steps 606 to 618are repeated until Vm is found to have a value of 1.04 in step 618. WhenVm is found to be equal to 1.04, the values of the three-dimensionalarray are interpolated to find the maximum of the maxima peaks, 620. Theresulting coordinates of the maximum of maxima peaks provide the finalvalues for the vertical multiplier, the horizontal multiplier and therotational angle for best alignment of the manipulated marked image withthe correlation reference plane. The corresponding resulting values ofm* and n* of the maximum of maxima provide the offset displacements ofthe manipulated marked image relative to the correlation referenceplane. The manipulated marked image is then rescaled by the inverses(reciprocals) of the found vertical and horizontal multipliers. It isrotated by the inverse (negative) of the found angular rotation, and isoffset by the inverses (negatives) of m* and n*, 622. This completes thefine setting process of reorienting and resizing.

[0106] It will be apparent to those skilled in the art that either thecorrelation reference plane or the manipulated marked image can beresized and reoriented to bring one into alignment with the other. Thepreferred embodiment resizes and reorients the manipulated marked imageto bring it into alignment with the correlation reference plane, andhence into element-to-element alignment with the watermarking plane.

[0107] Detecting the Watermark in a Marked Image

[0108] The process of watermark detection is designed to produce avisibly recognizable small image as its end product. The recognizableend product is obtained in a procedure which depends upon the existenceand knowledge of the watermark based on the robust random sequence. Theprocess exploits the extremely sophisticated and not yet completelyunderstood pattern recognition capabilities of the human visual system.It is through this exploitation that defeating the imparted watermarkbecomes much more difficult. A small rectangular array, called aselector, is conceived to implement the detection process. The selectorarray size must be much smaller than the pixel array of the marked imageto which it is being applied. This is to allow overlaying the selectoron the image hundreds of times without overlapping. The selector arrayshould be made large enough that a pixel array having the samedimensions could contain a recognizable binary image. More complexembodiments use a color rather than binary image as a reference. Aselector having 32 rows and 128 columns is used in an embodimentdescribed herein. It is applied to a marked image that has more than onemillion pixels.

[0109] The selector is used to locate rectangular clusters of pixels inthe marked image and corresponding clusters of elements in thereconstituted watermarking plane. The clusters are randomly scatterednon-overlapping positions. Random scattering of the clusters is done tofurther frustrate attempts to defeat watermark protection. Each elementof the selector contains one or more devices associated with variablesthat serve to store partial results of the watermark detection scheme.One embodiment uses two selector devices, one called a “coincidencecounter” and the other a “non-coincidence counter.” All coincidencecounters and non-coincidence counters are set to a zero value before thedetection process is begun.

[0110] A variable, called a statistically related variable, is definedwhich statistically relates an attribute of an element being consideredto the attributes of its neighboring elements. For each pixel in themarked image a first variable is computed for that pixel and a secondvariable is computed for that pixel's corresponding element in thereconstituted watermarking plane. A positive test results when thecomputed first variable has the same result, or a nearly orstatistically deemed equivalent result, as the computed second variable.If the results are deemed to be different, the test result is deemed tobe negative. The first variable is recomputed and compared with thesecond variable for each of that pixel's color planes. The coincidencecounter associated with that selector element is incremented by unityfor each color plane producing a positive result and the non-coincidencecounter is incremented by unity for each color plane that produces anegative result. The purpose of each element's coincidence andnon-coincidence counters is to associate with that element a confidencelevel of the watermark's identification with the random sequence knownonly to the marker and/or the marking entity. The quantified confidencelevel for each element is derived from the values in that element'scoincidence and non-coincidence counters, and is called a coincidencevalue.

[0111] For a tristimulus color image and for each cluster of pixels, therange of each coincidence counter value is from zero to plus three. Azero is obtained if the test results were negative for all three colorplanes. A plus three is obtained if the test results were positive forall three planes. The range of each non-coincidence counter is also fromzero to plus three, but conversely, a zero is obtained if the testresults for all three planes were positive and a plus three is obtainedif the test results of all three planes were negative. The count in eachcoincidence counter is the accumulated sum of the counts of positiveresults for corresponding pixels at each cluster location, and the countin each non-coincidence counter is the accumulated sum of the counts ofnegative results for corresponding pixels at each cluster location. Acoincidence counter value larger than the value of its correspondingnon-coincidence counter is associated with a partial watermarkdetection. A composite of coincidence counter values greater than theircorresponding non-coincidence counter values for a preponderance of theselector's elements results from and corresponds with a detectedwatermark having a high confidence value.

[0112] In an embodiment the test results and/or the comparison areperformed by subtraction operations. In a particular embodiment theattribute used is the pixel's brightness values. The statisticalrelationship is in regard to the average brightness value of theneighboring pixels. In this case, watermark detection proceeds with thesteps shown in FIG. 7. A selector array size is selected, 702. In thisexample, the selector array size is 32 by 128 elements. All thecoincidence and non-coincidence counters are initialized by setting themto read zero, 704. A specified particular element of the selector isplaced on an initial position of the expanded watermarking plane, 706.The particular first element is often the selector element that is atits upper leftmost corner. This particular element also locates acorresponding pixel and its components in all the color planes of themarked image when the marked image is aligned with the expandedwatermarking plane.

[0113] The following portion of the detection schema is repeatediteratively for all selector elements, for all color planes of eachpixel, and for all selected clusters. The next two eight-bit integersare chosen from the regenerated robust random sequence, 708. When theschema is started for the first selector element, the next two eight-bitintegers chosen in this step 708 are actually the first two eight-bitintegers of the robust random sequence. The two eight-bit integers arescaled to form random horizontal and vertical offsets from the initialor previous selector location, and the selector is moved to thatposition, 710. The selector element sequence is reset to the coordinatesof the initial particular selector element, 711. This selector elementis used to locate the corresponding particular element in thewatermarking plane, 712. The average magnitude of its neighboringelements in the watermarking plane is computed, 713. In the example,this is the average of the magnitudes of the particular element'sneighbors that lie in an 11 by 11 square of elements with the particularelement at the center of the square. If the selector element is too nearan edge of the watermarking plane to be at the center of itsneighborhood, the square neighborhood is moved to encompass theparticular element's nearest 120 existing neighbors.

[0114] The next color plane is chosen, 714. In the beginning of thisiterative schema this next color plane is actually the first colorplane. In the case of a monochrome image this is the only color plane.The coordinates of the particular selector element are used to locate acorresponding pixel color component in this next color plane, 715. Theaverage brightness of the neighboring 120 pixel color components iscomputed, 716, in a manner identical to that stated above forwatermarking plane elements. The values of the particular watermarkingplane element and the corresponding pixel color component are comparedto their respective neighborhood averages. If both values are equal toor greater than their respective neighborhood averages, 717, or if bothvalues are less than their respective neighborhood averages, 718, thecoincidence counter of that particular selector element is incremented,719 a. If one value is less than its respective neighborhood average andthe other value is equal to or greater than its respective neighborhoodaverage, the non-coincidence counter of that particular selector elementis incremented, 719 b. The magnitude of the value in each coincidencecounter relative to the magnitude of the value in its correspondingnon-coincidence counter is associated with the probability of watermarksequence validation.

[0115] A determination is made if all color planes were chosen fortesting their corresponding brightness value with regard to itsneighboring average, 720. If not, the process returns to step 714 forchoosing the next color plane. Steps 715 to 720 are repeated for thiscolor plane. This is continued until step 720 indicates the all colorplanes are tested. When the last (or only) color-plane is tested, adetermination is made if every element for that selector was chosen,724. If not, the next selector element is chosen, 726. Generally, thenext element is the next right-wise adjacent element on that row. Ifthere is no next adjacent element on that row, the next element is theleft-most element in the next selector row. This next selector elementbecomes the new particular element. Steps 712-724 are repeated until allselector elements are chosen and tested. When it is determined in step724 that all elements have been chosen, a determination is made if allnon-overlapping selector locations have been chosen, 728. If not, steps708 through 728 are repeated for all selector elements and marked imagecolor planes. When it is determined in step 728 that all selectorlocations are tested, all coincidence counters have their test resultvalues.

[0116]FIG. 8 shows a random multiple totality of positions of theselector 810 in a selector plane 802 resulting from an implementation ofthe process of FIG. 7. FIG. 8 shows a watermarking plane 804 and threecolor planes 806-808 of the marked image. The first selector elementacted upon is often the top leftmost element 812 of the selector in eachof the selector positions. It is noted that although each selectorposition is randomly offset from previously chosen positions, thepositions do not overlap each other.

[0117] The values contained within each coincidence and non-coincidencecounter associates with their corresponding selector element aconfidence level of the watermark's identification with the randomsequence known only to the marker and/or the marking entity. Thewatermark is considered to be detected if a preponderance of thedifferences of coincidence counter values less their respectivenon-coincidence counter values are non negative. Thus, an examination ofthe totality of these non negative differences explicitly suffices fordeclaring the watermark detected or not detected. Indeed, this can beconsidered as the end of the watermark detection technique.

[0118] Those skilled in the art will recognize that it is possible tomathematically derive a “probability of watermark detection,” in whichthe “probability of watermark detection” is greater than zero and lessthan one (where a value zero represents certainty of the absence of awatermark and a value one represents certainty of its presence), basedonly on the coincidence and non-coincidence counter values and assumingonly the property of uniform distribution of the random brightnessmultiplying factors. However, alternative embodiments recognize that a“preponderance” of differences being non negative is an inexact measure,at best. Clearly, if only a simple majority of the differences are nonnegative, whether the watermark is detected or not is at best a judgmentcall. Most likely it would be conceded as not having been a detection.To assist in this judgment, the present invention exploits the abilityof the human visual system to recognize a pattern in a cluttered field.This is accomplished by forming a binary image called a visualizer. Thevisualizer is formed to have the same dimensions as the selector (e.g.,32×128 pixels). A clearly recognizable pattern is placed into thevisualizer. A typical visualizer pattern is shown in FIG. 9, 900. Theblack border surrounding the visualizer is not considered to be part ofthe visualizer pattern. The pattern is an arrangement of blocks of blackand white pixels forming an easily recognizable pattern. A typicalpixel, 902, is at the lower ending of the image of a C. The visualizerimage is entirely white except for pixels making the letters IBM, 904,the copyright logo, 906, and the visualizer frame, 908.

[0119] The visualizer pattern is used to provide a visual image of theactual degree of “preponderance” of coincidence counters being nonnegative. The method steps diagrammed in FIG. 10 are used to provide awatermark signature in relation to the visualizer pattern. The watermarksignature is derived by using the visualizer pattern in combination withthe coincidence counter difference data to form what is herein referredto as the ‘visualizer-coincidence image’.

[0120] In one embodiment, the visualizer-coincidence image is formedwith the steps shown in FIG. 10. A visualizer pattern is formed having apixel array equal in size to the element array of the selector, 1002.The visualizer array consists of white and black pixels, where white isgiven the value one and black the value zero. All elements of theselector array will be examined to determine the pixel content of thevisualizer-coincidence image. To do this, the selector element sequenceis reset and the first element of the sequence is chosen, 1004. For thechosen selector element, the count in its corresponding non-coincidencecounter is subtracted from the count in its corresponding coincidencecounter, forming a difference, 1006. The sign of the difference istested, 1008, and if it is negative the corresponding pixel of thevisualizer is inverted (white is changed to black, and black to white)and placed into the corresponding pixel of the visualizer-coincidenceimage, 1010 b. If the sign is positive, the corresponding pixel of thevisualizer is placed unmodified into the corresponding pixel of thevisualizer-coincidence image, 1010 a. The selector element sequence istested to see if all elements have been chosen, 1012, and if not, thenext element is chosen, 1014, and steps 1006 to 1012 are repeated. Ifall selector elements have been chosen, the visualizer-coincidence imageis displayed, 1016. A judgment is made as to whether the pattern in thevisualizer-coincidence image is recognized as a reproduction of thevisualizer pattern, 1018. If it is recognized, the watermark ispositively detected, 1020 a. If not, the watermark is not detected, 1020b.

[0121] It is evident to those skilled in the art that if only the signof the difference between the count in a coincidence counter less thecount in its corresponding non-coincidence is to be used in constructingthe visualizer-coincidence image, then only one counter would have beenneeded for each selector element. In that case, step 719 a of FIG. 7would read “Increment the counter of Selector's Element,” and step 719 bwould read “Decrement the counter of Selector's Element.”

[0122]FIG. 11 shows a detection, 1102, resulting from the visualizer ofFIG. 8 for an imparted watermark made at a modulation strength of 1%. Aspreviously stated in all cases the black border is not part of thevisualizer-coincidence image. A stronger replication of the visualizer,1202, resulting for an imparted watermark made at a modulation strengthof 2% is shown in FIG. 12. A still stronger replication of thevisualizer, 1302, resulting for an imparted watermark made at amodulation strength of 4% is shown in FIG. 13.

[0123] An attempt to detect a watermark in an image that does not haveone, or in an image for which the watermarking plane cannot bereconstituted, produces a visualizer pattern that is an unrecognizablerandom melee. FIG. 14 shows a typical visualizer-coincidence image,1402, when a watermark is not detected. This results when manyvisualizer pixels are subjected to inversion. A preponderance of pixelsnot requiring inversion indicates watermark detection. This method infact has an extremely low probability of false-positive detection. Evenin a highly textured marked image, the visualizer pattern should beclearly recognizable to signify a watermark detection of very highcredibility.

[0124] Clearly, more information is present in the coincidence andnon-coincidence counter values than has been exploited above, where onlythe algebraic sign of their difference has been used. An alternativemethod of converting the visualizer image into a visualizer-coincidenceimage uses the magnitude of each coincidence counter value and that ofits corresponding non-coincidence counter. If C(i′, j′) is the value ofthe coincidence counter associated with selector element i′, j′ andC′(i′, j′) is the value of the corresponding non-coincidence counter,then the normalized magnitude of their difference e(i′,j′) is:

(i′, j′)=C(i′j′)/[C(i′, j′)+C′(i′, j′)]  (17)

[0125] when

C(i′, j′)+C′(i′, j′)>0,  (18)

[0126] and:

e(i′, j′)=1/2,  (19)

[0127] when

C(i′,j′)+C′(i′, j′)=0.  (20)

[0128] In this case, the visualizer image is converted into avisualizer-coincidence image by replacing each pixel in the visualizerimage with the corresponding value of e(i′, j′), when the visualizerpixel value is one; and by 1−e(i′, j′), when the visualizer pixel valueis zero. Notice that the visualizer-coincidence image is no longer abinary image, but includes gray shades ranging from black to white. Thejudgment as to whether the pattern placed in the visualizer isrecognizable in the visualizer-coincidence image is the same as before,and an attempt to detect the presence of a known watermark in an imagenot having one, or in an image having one but for which the watermarkingplane cannot be precisely reconstituted, also still produces anunrecognizable random melee in the visualizer-coincidence image.

[0129] Thus, this scheme makes more use of the actual values in thecoincidence and non-coincidence counters. It still employs a black andwhite element visualizer image pattern wherein each element is eitherblack or white (zero or one). However, the resulting elements of thevisualizer-coincidence image have values ranging between zero and onesuch that when displayed it has various levels of shades of gray. Thegray level depends on the counter data.

[0130] An embodiment of this alternative scheme is shown in FIG. 15. Avisualizer pattern is formed having a pixel array equal in size to theelement array of the selector, 1502. The visualizer array consists ofwhite and black pixels, where white is given the value one and black thevalue zero. All elements of the selector array will be examined todetermine the pixel content of the visualizer-coincidence image. To dothis, the selector element sequence is reset and the first element ofthe sequence is chosen, 1504. For the chosen selector element, the ratioof the count in its corresponding coincidence counter to the sum of theif counts in its corresponding coincidence and non-coincidence countersis computed, 1506. The color of the corresponding visualizer pixel istested, 1508, and if it is black, the ratio subtracted from one isplaced into the corresponding pixel of the visualizer-coincidence image,1510 a. If the visualizer pixel is white, the ratio is placed unmodifiedinto the corresponding pixel of the visualizer-coincidence image, 1510b. The selector element sequence is tested to see if all elements havebeen chosen, 1512, and if not, the next element is chosen, 1514, andsteps 1506 to 1512 are repeated. If all selector elements have beenchosen, the visualizer-coincidence image is displayed as a high contrastmonochrome image, 1516. A judgment is made as to whether the pattern inthe visualizer-coincidence image is recognized as a reproduction of thevisualizer pattern, 1518. If it is recognized, the watermark ispositively detected, 1520 a. If not, the watermark is not detected, 1520b.

[0131] The Implementation of Brightness Modification by Addition Insteadof Multiplication

[0132] An alternative, and equivalent, form for modifying pixelbrightness is to change the brightness by adding to or subtracting fromthe component Y(i, j) a different small random value ε(i, j). As beforestated, 1≦i≦I and 1≦j≦J are the row and column indices of the pixellocation in the image. To help make the brightness variation lessvisible, ε(i, j) is made proportional to the original brightness of thecomponent, thereby making the change smaller in darker areas of theimage where the human eye is more discerning of changes in brightness.Thus, ε(i, j)=δ(i, j)Y(i, j), where δ(i, j) is a value selected from anarray of random values that may have the range −0.5<δ(i, j)<0.5. Themodified component Y′(i, j)=Y(i, j)+ε(i, j)=Y(i, j)+δ(i, j)+δ(i, j). Toalter only the brightness of each pixel in a color image, the ratios ofits components must be preserved. If the color components of theunaltered pixel are X(i, j), Y(i, j), and Z(i, j), and the colorcomponents of the brightness altered pixel are X′(i, j), Y′(i, j), andZ′(i, j), then X′(i, j)/X(i, j)=Z′(i, j)/Z(i, j)=Y′(i, j)/Y(i,j)=1+δ+(i, j). It is evident that this is equivalent to multiplying thebrightness of the each color component by 1+δ(i, j), since X′(i, j)=X(i,j)[1+δ(i, j)], Z′(i, j)=Z(i, j)[1+δ(i, j)], and Y′(i, j)=Y(i, j)[1+δ(i,j)]. If the random values 1+δ(i, j) are set equal to w(i, j) as definedbefore, the two methods are identical. In summary, the modification ofpixel brightness by an additive value that is proportional to pixelbrightness while preserving the ratios of the color components of thepixel is equivalent to modifying the brightness of the pixel bymultiplication. An additive and multiplicative modulation can have adifferent effect only if the ratios of the color components of the pixelare allowed to change.

[0133] Using a Blurring Filter Before Attempting Watermark Detection toImprove the Probability of Detection

[0134] Watermark detection may be enhanced in accordance with thepresent invention as described hereinafter in a manner that is adaptablefor use of any of many watermarking techniques. It is most particularlyadaptable to a watermarking technique employing a watermarking plane.Thus, although the enhancement of the detection technique is adaptableto many watermarking techniques, it is most easily described andadaptable to the watermark imparting and detecting methods describedpreviously herein.

[0135] As described above for particular embodiments, watermarks areimparted into an image by multiplying the components of each pixel ofthe image by the linearly remapped values of the watermarking plane,w(i, j), where 1>w(i, j)≧(1−2β), i is the value's row index, j is thevalue's column index, and β is the modulation strength of the watermark.Additionally, all elements in the generated watermarking plane, treatedas an ensemble, are adjusted to have a mean and median of 1−β. In otherwatermark embodiments this is accomplished by addition and/orsubtraction operations.

[0136] A method for improving the detection of the imparted watermark ina marked image and, more specifically, in a derived copy of a markedimage employs use of a two-dimensional blurring filter prior to anattempted detection. A blurring filter is also called a low-pass filterin signal-processing terminology. Application of the blurring filter isadvantageous in that it reduces high-frequency noise content among thecolor components in the marked image while leaving low-frequency contentrelatively unaltered.

[0137] In the example embodiment, since the watermark, as imparted intothe image, has the appearance and behavior of a two-dimensional noisepattern itself, any addition of high-frequency noise can potentiallypartially obscure the watermark and make it more difficult to detect.This is specifically the case if a derived copy is produces by scanninga printed copy of a marked image. Substantial high-frequency noise isadded to a marked image by the screening process used in preparation forits printing. Printing ordinarily is accomplished with one or severalinks or dyes that each have an invariable color. The screening processproduces various shades of the invariably colored inks or dyes, neededto reproduce the color components, by covering the spatial arearepresented by each pixel with a finer grids of dots of the inks ordyes. Each of the grids of dots has a varying spatial density of theinks or dyes, and each dot in a grid of dots is significantly smallerspatially than the pixel area. The grids of dots so produced, one foreach color component, spatially replace the pixel they represent in theprinted image copy, and, after fusion by the human viewing system,collectively produce a perceived correct color of the pixel.

[0138] The screening process, by converting the components of each pixelinto grids of dots of still smaller dimensions, inherently addshigh-frequency artifacts and noise to the printed image copy that werenot in the original image. This can be verified easily by viewing aprinted image under moderate magnification. If the printed image is thenscanned to produce a derivative digitized image, the addedhigh-frequency noise reproduced in the derivative copy is detrimental towatermark detection. It is to reduce the detrimental effects of theadded high-frequency that a blurring filter is used. As stated above inthe subsection titled “The Property of Explicit Low Frequency Content”the watermarking plane is designed to have significant low frequencycontent and will thus be relatively immune to the action of a blurringfilter, but the high-frequency content of image, and more importantlythe added noise, will be substantially attenuated.

[0139] An example rudimentary blurring filter can be implemented in thefollowing manner. Each color plane of the image, represented as arectangular array of like color components, is partitioned, right toleft and top to bottom, into small sub-arrays that are three pixels highand three pixels wide. If the number of pixels in a row or column of theimage array is not evenly divisible by three, the edge sub-arrays at theright or bottom of the partitioned image will contain fewer than ninepixels. The color components of the nine pixels in each sub-array (orfewer than nine if the sub-array is an edge sub-array) are averaged. Theaverage value of the color components in each sub-array is then used toreplace all the values in that sub-array. This completes thetwo-dimensional blurring filter. Those skilled in the art will recognizethat there many other more sophisticated ways to implement atwo-dimensional blurring filter. Nevertheless, in the method of thepresent invention the important desired result of applying any blurringfilter remains the same as the that of applying the rudimentary filterdescribed here, namely, the reduction of high spatial frequencies andthe preservation of low spatial frequencies of features in thederivative image.

[0140] In the example rudimentary blurring filter presented, the firststep of the method was to divide a marked image's color plane into nineelement square sub-arrays. The choice of the size of the sub-arraysdetermines the degree to which high spatial frequencies among the pixelcomponents in the marked image are reduced in the filtered image, if themarked image contains such high spatial frequencies, which it may not.By using nine element sub-arrays, the highest spatial frequency that canpossibly exist in the filtered image is reduced by a factor of three.The larger the sub-array is chosen, the greater is the reduction of thehighest possible spatial frequency that can exist in the filtered image.It will be apparent to those skilled in the art that, when applying ablurring filter, the degree to which the highest spatial frequency is tobe reduced depends upon the degree to which high-frequency content inthe watermarking plane used to produce the marked image was reduced. Ifthe objective of using the blurring filter it to improve watermarkdetection, it would become counter productive to reduce thehigh-frequency content of the marked image by a factor greater than thatused in creating the watermarking plane; to do so would remove not onlyundesirable high-frequency noise in the marked image but also some ofthe information contained in the imparted watermark.

[0141] Referring to FIG. 16, a highly enlarged segment of an examplewatermarked image is shown. The watermark was imparted according to themethod described previously herein. The modulation strength, β, used forthe marking was 2.5 percent and visibility of the watermark, even athigh magnification is classified as undetectable invisible. Referring toFIG. 17, a similarly enlarged segment of a derivative image is shown; itis derived from the marked image shown in FIG. 16 after it is screenedin preparation for printing, forming a screened image, and subsequentlyprinted and scanned. Note that significant high-frequency noiseresulting from the screening process is evident in FIG. 17. FIG. 18shows a filtered image produced by applying the rudimentary blurringfilter to the derived image. The noise reduction resulting fromapplication of the blurring filter is evident by comparing FIG. 18,after the application, with FIG. 17, before the application.

[0142] Watermark detection was attempted for each of the three images,the enlarged segments of which are shown in FIGS. 16, 17, and 18. Thewatermark visualizer-coincidence images realized form the detectionusing the original marked image is shown in FIG. 19. The detection is aperfect detection. The original marked image is then screened forprinting, printed and scanned to form the derivative image. Thewatermark visualizer-coincidence image realized form the detection usingthe derivative image is shown in FIG. 20. The detection is very weak,nearly nonexistent. After the rudimentary blurring filter is applied tothe derivative image to form the filtered image, watermark detection isagain attempted. The watermark visualizer-coincidence image realizedform the detection using the filtered image is shown in FIG. 21. Thedetection, although imperfect, is very strong, testifying to theefficacy of the use of the blurring filter before attempting watermarkdetection.

[0143] Use of a blurring filter is advantageous before any attemptedwatermark detection, regardless of the robust watermarking method used.If a watermark is robust, that is, if it is resistant to attacks, itmust ordinarily contain significant low-frequency content. Thelow-frequency content of the watermark will not be unduly disturbed bythe blurring filter, since the blurring filter is by its nature alow-pass filter. Any detection-disturbing high-frequency content in theimage, whether occurring naturally as a part of the image or whetheradded by artificial means, such as screening in preparation forprinting, will be suppressed by the action of the blurring filter. Theactual amount of blurring is generally dependent upon the particularapplication and/or watermark. This is determined in ways known to thoseskilled in the art.

[0144] Although the description is made for particular embodiments,techniques and arrangements, the intent and concept of the presentinvention are suitable to other embodiments, techniques andarrangements. For example, an obvious choice, and the choice of lastresort, in demonstrating the existence of a watermark in a manipulatedmarked image is to again impart the watermark onto a copy of theunmarked original digitized image, and to use the color planes of thatreconstituted marked image as ideal substitutes for the watermarkingplane. The disadvantage of this alternative method is that it requiresaccess to a copy of the unmarked original image. The visualizer can alsohave multiple color planes. The visualizer can be employed without theselector by having at least one statistical value associated with eachpixel of the visualizer. Also, sequential repositioning of the selectoron the reconstituted watermarking plane need not be non-overlapping.Non-overlapping selector positions in the presented embodiment representonly a computational simplification. Also, a small random but coherentimage may be included in the watermarking plane at positions known onlyto the marker and/or marking entity; if the so constituted watermarkingplane were imparted onto a uniform color plane with strong modulationstrength, the coherent image would be visible without use of avisualizer. Other methods of watermark detection and/or demonstrationmay be employed. These may for instance utilize any of the manystatistical relationships between elements and their neighbors ornon-neighbors. The robust techniques presented here may be used incombination with visible watermarking techniques as well as fragileinvisible techniques. It will be clear to those skilled in the art thatother modifications to the disclosed embodiments can be effected withoutdeparting from the spirit and scope of the invention.

[0145] The present invention can also be realized in embodiments of anapparatus having mechanisms for implementing the methods of the presentinvention as described herein in manners known to those skilled in theart. For example, the present invention can also be realized as anapparatus to impart a watermark onto a digitized image, said apparatuscomprising: means for providing a digitized image having at least oneimage plane, said image plane being represented by an image array havinga plurality of pixels, said pixel having at least one color component,said watermark being formed using a distinct watermarking planerepresented by an array having a plurality of distinct watermarkingelements, each of said distinct watermarking elements having an arrayposition and having one-to-one positional correspondence with said imagepixels; and means for multiplying said brightness data associated withsaid at least one color component by a predetermined brightnessmultiplying factor, wherein said brightness multiplying factor is acorresponding distinct watermarking element, said distinct watermarkingelement being in the domain of 0.5 to 1.0. Thus in an embodiment thepresent invention can also be realized as an apparatus for imparting awatermark onto a digitized image comprising the steps of: means forproviding said digitized image comprised of a plurality of pixels,wherein each of said pixels includes brightness data that represents abrightness of at least one color; and means for multiplying saidbrightness data associated with at least one of said pixels by apredetermined brightness multiplying factor in the domain of 0.5 to 1.0.In a particular embodiment of the apparatus the image has I rows and Jcolumns, and has a pixel in row i and column j having a brightness Y(i,j), and the means for multiplying includes: means for adding to orsubtracting from the brightness Y(i, j) a different small random valueε(i, j), wherein 1≦i≦I and 1≦j≦J are the row and column indices of apixel location in the image.

[0146] Thus in an embodiment the present invention can also be realizedas an apparatus for imparting a watermark onto a digitized imagecomprising: means for providing said digitized image comprised of aplurality of pixels, wherein each of said pixels includes brightnessdata that represents a brightness of at least one color, with said imagehaving I rows and J columns, and a pixel in row i and column j having abrightness Y(i, j); and means for adding to or subtracting from thebrightness Y(i, j), for all i and all j, a random value ε(i, j), wherein1≦i≦I and 1≦j≦J are the row and column indices of a pixel location inthe image.

[0147] Thus in an embodiment the present invention can also be realizedas an apparatus for generating a watermarked image, the apparatuscomprising: means for imparting a watermark onto a digitized imagehaving a plurality of original pixels, each of said pixels havingoriginal brightness values; means for providing said digitizedwatermarking plane comprising a plurality of watermarking elements, eachelement having a watermark brightness multiplying factor and havingone-to-one positional correspondence with said original pixels; andmeans for producing a watermarked image by multiplying said originalbrightness values of each of said original pixels by said brightnessmultiplying factor of a corresponding one of said watermark elements.

[0148] Thus in an embodiment the present invention can also be realizedas an apparatus comprising: means for forming a watermarking planeincluding a plurality of elements each having a brightness adding orsubtracting value; means for generating a robust random sequence ofintegers having a first plurality of bits; means for linearly remappingsaid random sequence to form a remapped sequence of brightnessmultiplying factors to provide a desired modulation strength; means forcomputing a discrete Fourier transform of said remapped sequence to forma Fourier sequence having frequency coordinates; means for expandingsaid frequency coordinates to form an expanded sequence; means forcomputing an inverse Fourier transform of said expanded sequence toobtain a watermarking sequence of values; and means for deriving saidbrightness adding or subtracting values of said elements of saidwatermarking plane based upon said watermarking sequence of values.

[0149] Thus in an embodiment the present invention can also be realizedas an apparatus for detecting a watermarking plane comprising: means forproviding an image having a plurality of pixels marked by thewatermarking plane, said watermarking plane having a plurality ofwatermarking elements; means for aligning said watermarking plane withsaid image; means for identifying a subset of said image pixels; meansfor each image pixel, u(i, j), wherein 1≦i≦I and 1≦j≦J, of said subsetof image pixels, including means for generating a first valuerepresenting a relationship between an attribute of said image pixelu(i, j) and an attribute of image pixels that neighbor said image pixelu(i, j); means for identifying a watermarking element w(i, j) thatpositionally corresponds to said image pixel u(i, j) and watermarkingelements that correspond to said image pixels that neighbor said imagepixel u(i, j); means for generating a second value representing arelationship between an attribute of said watermarking element w(i, j)and an attribute of the identified neighboring watermarking elements;and means for generating a coincidence value representing likelihoodthat said image is marked by said watermarking plane based upon saidfirst and second values.

[0150] Thus in an embodiment the present invention can also be realizedas an apparatus comprising means for generating a visual representationof a data array of data elements having a data array size, including:means for providing a visualizer-coincidence pattern ofvisualizer-coincidence image pixels represented by avisualizer-coincidence array of visualizer-coincidence pixels, saidvisualizer-coincidence array having an array size equal to said dataarray size, wherein each of said visualizer-coincidence pixels has afirst color if a corresponding data element is a first logical value anda second color if said corresponding data element has a complementarylogical value; means for setting said visualizer-coincidence pixel to afirst color if a value of said data element is above a predeterminedthreshold and to another color if said value is below said predeterminedthreshold; and means for displaying said visualizer-coincidence image toform said visual representation.

[0151] Thus in an embodiment the present invention can also be realizedas an apparatus for imparting a watermark onto a digitized imagecomprising: means for providing said digitized image comprised of aplurality of pixels, wherein each of said pixels includes brightnessdata represented by at least one color component, Y; and means foradding to or subtracting from said brightness data associated with atleast one of said pixels a predetermined brightness adding orsubtracting factor in the range of −0.5Y to +0.5Y, wherein saidbrightness adding or subtracting factor has a relationship with a numbertaken from a random number sequence, said relationship is a linearremapping to provide a desired modulation strength, and said modulationstrength is less than 50 percent.

[0152] Thus in an embodiment the present invention can also be realizedas an apparatus for imparting a watermark onto a digitized imagecomprising: means for providing said digitized image comprised of aplurality of pixels, wherein each of said pixels includes brightnessdata represented by at least one color component, Y; and means foradding to or subtracting from said brightness data associated with atleast one of said pixels by a predetermined brightness adding orsubtracting factor in the range of −0.5Y to +0.5Y, wherein saidbrightness adding or subtracting factor has a relationship with a numbertaken from a random number sequence, said relationship is a linearremapping to provide a desired modulation strength, said sequence isformed from a plurality of robust watermarking parameters, and saidparameters comprise a cryptographic key, two coefficients and an initialvalue of said random number generator.

[0153] The present invention can be realized in hardware, software, or acombination of hardware and software. A visualization tool according tothe present invention can be realized in a centralized fashion in onecomputer system, or in a distributed fashion where different elementsare spread across several interconnected computer systems. Any kind ofcomputer system—or other apparatus adapted for carrying out the methodsand/or functions described herein—is suitable. A typical combination ofhardware and software could be a general purpose computer system with acomputer program that, upon being loaded and executed, controls thecomputer system such that it carries out the methods described herein.The present invention can also be embedded in a computer programproduct, which comprises all the features enabling the implementation ofthe methods described herein, and which—when loaded in a computersystem—is able to carry out these methods.

[0154] Computer program means or computer program in the present contextinclude any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or aftereither or both of the following: conversion to another language, code ornotation, and/or reproduction in a different material form.

[0155] Thus the invention includes an article of manufacture comprisinga computer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the article of manufacture comprisescomputer readable program code means for causing a computer to effectthe steps of a method of this invention. Similarly, the presentinvention may be implemented as a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the computer program product comprisescomputer readable program code means for causing a computer to effectone or more functions of this invention. Furthermore, the presentinvention may be implemented as a program storage device readable bymachine, tangibly embodying a program of instructions executable by themachine to perform method steps for causing one or more functions ofthis invention.

[0156] It is noted that the foregoing has outlined some of the morepertinent objects and embodiments of the present invention. Thisinvention may be used for many applications. Thus, although thedescription is made for particular arrangements and methods, the intentand concept of the invention is suitable and applicable to otherarrangements and applications. It will be clear to those skilled in theart that modifications to the disclosed embodiments can be effectedwithout departing from the spirit and scope of the invention. Thedescribed embodiments ought to be construed to be merely illustrative ofsome of the more prominent features and applications of the invention.Other beneficial results can be realized by applying the disclosedinvention in a different manner or modifying the invention in ways knownto those familiar with the art.

What is claimed is:
 1. A method for imparting a watermark onto adigitized image, said method comprising: providing a digitized imagehaving at least one image plane, said image plane being represented byan image array having a plurality of pixels, said pixel having at leastone color component, said watermark being formed using a distinctwatermarking plane represented by an array having a plurality ofdistinct watermarking elements, each of said distinct watermarkingelements having an array position and having one-to-one positionalcorrespondence with said image pixels, and multiplying said brightnessdata associated with said at least one color component by apredetermined brightness multiplying factor, wherein said brightnessmultiplying factor is a corresponding distinct watermarking element, andsaid watermark has a invisibility classification.
 2. A method as recitedin claim 1, wherein said brightness multiplying factor has arelationship with a number taken from a random number sequence.
 3. Amethod as recited in claim 2, wherein said relationship is a linearremapping to provide a desired modulation strength.
 4. A method asrecited in claim 3, wherein said modulation strength lies in the domaingreater than or equal to zero and less than or equal to 0.5.
 5. A methodfor imparting a watermark onto a digitized image comprising the stepsof: providing said digitized image comprised of a plurality of pixels,wherein each of said pixels includes brightness data that represents abrightness of at least one color; and altering said brightness dataassociated with a plurality of said pixels maintaining the hue andsaturation of said pixel.
 6. A method as recited in claim 5, whereinsaid image has I rows and J columns, and has a pixel in row i and columnj having at least one brightness, Y(i, j), and the step of alteringincludes: adding to or subtracting from the brightness Y(i, j) adifferent small random value ε(i, j), wherein 1≦i≦I and 1≦j≦J are therow and column indices of a pixel location in the image.
 7. A method asrecited in claim 6, wherein the step of adding to or subtracting fromincludes making ε(i, j) proportional to an original brightness of thepixel.
 8. A method as recited in claim 6, wherein color components ofthe unaltered pixel are X(i, j), Y(i, j), and Z(i, j), and colorcomponents of the brightness altered pixel are X′(i, j), Y′(i, j), andZ′(i, j), and the step of adding to or subtracting from includes settingε(i, j)=δ(i, j)Y(i, j), where δ(i, j) is a value selected from an arrayof random values within a range of 0≦δ(i, j)≦1, such that the modifiedbrightness Y′(i, j)=Y(i, j)+ε(i, j)=Y(i, j)+δ(i, j)Y(i, j), and X′(i,j)/X(i, j)=Z′(i, j)/Z(i, j)=Y′(i, j)/Y(i, j)=ε(i, j)=1−δ(i, j).
 9. Amethod as recited in claim 8, wherein the step of setting includespreserving ratios of color components in each pixel.
 10. A method asrecited in claim 9, wherein the step of preserving includes settingX′(i, j)/X(i, j)=Z′(i, j)/Z(i, j)=Y′(i, j)/Y(i, j)=1−δ(i, j), whereinthe color components of the unaltered pixel are X(i, j), Y(i, j), andZ(i, j), and the color components of the brightness altered pixel areX′(i, j), Y′(i, j), and Z′(i, j).
 11. A method for imparting a watermarkonto a digitized image comprising the steps of: providing said digitizedimage comprised of a plurality of pixels, wherein each of said pixelsincludes brightness data that represents a brightness of at least onecolor, with said image having I rows and J columns, and a pixel in row iand column j having a brightness Y(i, j); and for a plurality i and atleast one j adding to or subtracting from the brightness Y(i, j) arandom value ε(i, j), wherein 1≦i≦I and 1≦j≦J are the row and columnindices of a pixel location in the image.
 12. A method as recited inclaim 11, wherein ε(i, j) is in the domain 0 to 1 multiplied by Y(i, j).13. A method for generating a watermarked image, the method comprising:imparting a watermark onto a digitized image having a plurality oforiginal pixels, each of said pixels having at least one original pixelbrightness value; providing said digitized watermarking plane comprisinga plurality of watermarking elements, each element having a watermarkbrightness multiplying factor and having one-to-one positionalcorrespondence with said original pixels; and producing a watermarkedimage by multiplying said original brightness of each of said originalpixels by said brightness multiplying factor of a corresponding one ofsaid watermark elements.
 14. A method comprising: forming a watermarkingplane including a plurality of elements each having a brightness addingor subtracting factor, including the steps of: generating a securerandom sequence of integers having a first plurality of bits; linearlyremapping said random sequence to form a remapped sequence of brightnessmultiplying factors to provide a desired modulation strength; computinga discrete Fourier transform of said remapped sequence to form a Fouriersequence having frequency coordinates; expanding said frequencycoordinates to form an expanded sequence; computing an inverse discreteFourier transform of said expanded sequence to obtain a watermarkingsequence of values; and deriving said brightness adding or subtractingvalues of said elements of said watermarking plane based upon saidwatermarking sequence of values.
 15. A method for detecting a watermarkin a marked image, said method comprising: providing said marked imagemarked by a watermarking plane, said marked image having at least onecolor plane including a plurality of image pixels, said watermarkingplane having a plurality of watermarking elements, wherein each of saidimage pixels has at least one brightness value and each of saidwatermarking elements has a brightness adding and/or subtracting factor,including the steps of: (a) reconstructing said watermarking plane; (b)aligning said watermarking plane with said marked image such that eachwatermarking element has a corresponding image pixel; (c) providing aselector array and a visualizer image of equal size, wherein saidselector array has a plurality of selector elements each having at leastone counter, and wherein said visualizer image has a plurality ofvisualizer pixels each having at least one brightness value, and whereinsaid visualizer pixels represent a recognizable pattern when displayed;(d) resetting said at least one counter to zero; (e) placing saidselector in an initial position by aligning said selector elements witha plurality of corresponding image pixels and a plurality ofcorresponding watermarking elements; (f) choosing a selector element andidentifying a corresponding watermarking element; (g) identifying afirst plurality of watermarking elements that neighbor saidcorresponding watermarking element; (h) generating a first average thatrepresents an average of brightness multiplying factors of said firstplurality of watermarking elements; (i) choosing a color plane of saidmarked image and finding a corresponding image pixel; (j) identifying afirst plurality of neighboring pixels that neighbor said correspondingimage pixel; (k) generating a second average that represents an averageof brightness values of said first plurality of neighboring pixels; (l)updating said at least one counter based upon first and secondcomparison operations, wherein said first comparison operation comparessaid first average with said brightness multiplying factor of saidcorresponding watermarking element and said second comparison operationcompares said second average with said brightness value of saidcorresponding pixel; (m) repeating steps (i) through (l) for all colorplanes; (n) repeating steps (f) through (m) for all selector elements;(o) choosing a new selector position that does not overlap any previousselector position; (p) repeating steps (f) through (o) for allnon-overlapping selector positions; and (q) generating a visualrepresentation indicating detection of said watermark in said markedimage utilizing said at least one counter of said selector array andsaid visualizer pixels.
 16. A method for detecting a watermarking planecomprising the steps of: providing an image having a plurality of imagepixels, u(i, j), with said image having I rows and J columns, and apixel in row i and column j having at least one component, marked by awatermarking plane; said watermarking plane having a plurality ofwatermarking elements, w(i, j), with said watermarking plane having Irows and J columns, and an element in row i and column j having abrightness multiplying factor; aligning said watermarking plane withsaid image; identifying a subset of said image elements; for each pixel,u(i, j), of said subset of image pixels, generating a first valuerepresenting a relationship between an attribute of said pixel u(i, j)and an attribute of image pixels that neighbor said pixel u(i, j);identifying a watermarking element, w(i, j), that corresponds to saidpixel u(i, j) and watermarking elements that correspond to said imagepixels that neighbor said image pixel u(i, j); generating a second valuerepresenting a relationship between an attribute of said watermarkingelement w(i, j) and an attribute of the identified watermarkingelements; and generating a coincidence value representing a likelihoodthat said image is marked by said watermarking plane based upon saidfirst and second values.
 17. A method as recited in claim 1, whereinsaid distinct watermarking element, has a value being in the domaingreater than or equal to zero and less than or equal to one.
 18. Amethod for imparting a watermark onto a digitized image comprising thesteps of: providing said digitized image comprised of a plurality ofimage pixels with said digitized image having I rows and J columns, anda pixel in row i and column j having at least one component, Y(i, j);and adding to or subtracting from said brightness data associated withat least one of said pixels a predetermined brightness adding factor inthe range of 0 to Y(i, j), or brightness subtracting factor in the rangeof 0 to Y(i, j), wherein said brightness adding or subtracting factorhas a relationship with a number taken from a random number sequence,said relationship is a linear remapping to provide a desired modulationstrength, and said modulation strength is less than or equal to 50percent.
 19. A method for imparting a watermark onto a digitized imagecomprising the steps of: providing said digitized image comprised of aplurality of image pixels with said image having I rows and J columns,and a pixel in row i and column j having at least one component, Y(i,j); and adding to or subtracting from said brightness data associatedwith at least one of said pixels by a predetermined brightness adding orsubtracting factor in the range of 0 to Y(i, j), wherein said brightnessadding or subtracting factor has a relationship with a number taken froma random number sequence, said relationship is a linear remapping toprovide a desired modulation strength, said sequence is formed from aplurality of robust watermarking parameters, and said parameterscomprise a cryptographic key, two coefficients and an initial value ofsaid random number generator.
 20. A method for detecting a watermark,said method comprising: providing a marked image having a plurality ofimage pixels said marked image being marked by a watermarking plane,having a plurality of watermark elements; aligning said watermarkingplane with said marked image, and generating a coincidence value byaveraging a detection coincidence for each selector element of a groupof selector elements taken from said image pixels.
 21. A method asrecited in claim 20, wherein each of said group of selector elements hasa selector size, said method further comprising: providing a visualizerpattern having a plurality of visualizer pixels and a visualizer sizeequal to said selector size, each of said visualizer pixels beingassociated with one of said selector elements and having a visualizercolor; and displaying a watermark detection pattern having a size atleast equal to said visualizer size and a plurality ofvisualizer-coincidence pixels, wherein each of saidvisualizer-coincidence pixels is associated with a correspondingselector element and a corresponding visualizer pixel, and each of saidvisualizer-coincidence pixels being displayed having said visualizercolor when said coincidence value of said corresponding selected elementhas an indication of a detection success and having another colorotherwise.
 22. A method as recited in claim 20 wherein said watermark isbased on a factor multiplying a brightness value of each of said imagepixels.
 23. A method as recited in claim 20, further comprising:reconstructing said watermarking plane used in generating saidwatermark.
 24. A method as recited in claim 23, wherein saidwatermarking plane has a plurality of watermarking elements, said methodfurther comprising: rotating, resizing and said image to bring it to asize and position of an original image, and aligning said watermarkingplane with said marked image such that each of said watermarkingelements has a corresponding image pixel.
 25. A method as recited inclaim 20, wherein each said group contains 128 elements.
 26. A method asrecited in claim 20, wherein each pixel of said image pixels has amonochrome brightness value.
 27. A method as recited in claim 20,wherein said watermarking plane is generated using a plurality of robustwatermarking parameters.
 28. A method as recited in claim 20, whereinsaid coincidence variable is determined using a statistically relatedattribute relating each said selector element to a plurality ofneighboring elements.
 29. A method as recited in claim 28, wherein saidattribute is a brightness value.
 30. A method for detecting a watermarkimparted on an image, said method comprising: providing said imagehaving at least one image plane, said image plane being represented byan image array having a plurality of image elements, said watermarkbeing formed using a watermarking plane represented by a watermarkingarray having a plurality of watermarking elements, each of saidwatermarking elements having a first array position and havingone-to-one positional correspondence with said image elements; computinga first statistically related variable for each element of at least onefirst grouping of a first selector array of elements taken from saidimage elements, wherein each of said image elements has a second arrayposition; computing a second statistically related variable for eachelement of at least one second grouping of a second selector array ofelements taken from said watermarking elements, wherein each element ofsaid second selector array of elements has one-to-one positionalcorrespondence with said first selector array, and wherein saidcorrespondence forms combinations of corresponding elements; comparingto determine an affirmative and non-affirmative likeness of said firstand second statistically related variables for each of said combinationsof corresponding elements; and forming at least one comparison arrayhaving one-to-one correspondence with said at least one first groupingand having a plurality of comparison elements, wherein each of saidcomparison elements contains a positive detection indication for eachelement of said first grouping when said step of comparing results in anaffirmative likeness, and a negative detection indication for eachelement of said first grouping when said step of comparing results in anon-affirmative likeness.
 31. A method as recited in claim 30, whereinsaid watermark is formed by adding or subtracting a brightness factor ofeach of said image elements by an amount contained in a correspondingelement of said watermarking elements.
 32. A method as recited in claim30, wherein said first grouping corresponds to a selector positioned toencompass said first selector array of elements forming a rectangularcluster of elements.
 33. A method as recited in claim 30, wherein saidfirst statistical variable is formed by comparing an attribute of saideach element of said first selector array of elements to an averageattribute of its 128 closest neighbors.
 34. A method as recited in claim30, wherein said attribute is a ratio of the color component to theaverage of neighboring color components in the same color plane.
 35. Amethod as recited in claim 30, wherein each of said at least one firstgrouping is positioned so as not to overlap any other of said at leastone first grouping.
 36. A method as recited in claim 30, wherein eachsaid comparison elements has a particular position in said comparisonarray, said method further comprising: determining an average percentageof said affirmative and non-affirmative likeness of each element of saidcomparison elements having a same particular position in all arrays ofsaid at least one comparison array, and forming a detection array ofelements having one-to-one element correspondence with said comparisonelements, wherein each element of said detection array of elementscontains said average percentage.
 37. A method as recited in claim 36,further comprising the steps of: providing a visualizer pattern ofpixels represented by an array having visualizer pixels which haveone-to-one element correspondence with said detection array, each ofsaid visualizer pixels has a first logical value if a correspondingvisualizer pixel is black, and a complementary logical value if saidcorresponding pixel is white; forming a visualizer coincidence imagehaving a plurality of coincidence pixels, wherein a coincidence pixelhas a corresponding visualizer pixel and a corresponding detection arrayelement; and setting said coincidence pixel to black if both saidcorresponding visualizer pixel is black and said percentage average ofsaid corresponding detection array element has a value greater than apredetermined detection threshold, otherwise setting said coincidencepixel to white.
 38. A method as recited in claim 30, wherein said imagehas three color planes.
 39. A method comprising generating a visualrepresentation of a data array of data elements having a data arraysize, including the steps of: providing a visualizer pattern ofvisualizer pixels represented by a visualizer array of visualizerpixels, said visualizer array having a visualizer array size equal tosaid data array size; forming a visualizer-coincidence image of imagepixels represented by an image array having an image array size equal tosaid visualizer array size; setting each said visualizer-coincidencepixel to the color of said corresponding visualizer pixel if a value ofsaid corresponding data element is above a predetermined threshold andto another color if said value is below said predetermined threshold;and displaying said visualizer-coincidence image to form said visualrepresentation.
 40. A method as recited in claim 39, wherein said dataarray represents data resulting from a watermark detectionimplementation.
 41. A method as recited in claim 39, wherein said firstcolor is black and said second color is white.
 42. A method as recitedin claim 39, wherein said threshold is set at a fifty percent successrate.
 43. A method for demonstrating an existence of a watermark in amarked image, said image having a plurality of image pixels, said methodcomprising: providing a visualizer pattern represented by an array ofvisualizer elements, each of said visualizer elements corresponding withone pixel of a plurality of visualizer pixels and having a first valueif said one pixel has a first color and a second value if said one pixelhas a second color, said visualizer array having a visualizer arraysize; implementing a watermark detection scheme and computing acoincidence value for each of said image pixels within a plurality ofpixel selector arrays taken from among said image pixels, each of saidpixel selector arrays having a selector array size equal to saidvisualizer array size; forming a detection array from a plurality ofcoincidence values, wherein said detection array has a detection arraysize equal to said visualizer size; and computing a coincidencedetection value for each of said visualizer elements such that saiddetection value represents a visualizer.
 44. A method for detecting awatermark in a marked image having a plurality of image pixels, saidmarked image marked by a watermarking plane having a plurality ofwatermarking elements, said method comprising: providing a visualizerpattern having a plurality of visualizer pixels and a visualizer size;aligning said watermarking plane with said marked image such that eachsaid image pixel has a corresponding watermarking element; generating astatistically related variable for each image element in a plurality ofgroupings of image elements in relationship with said correspondingwatermarking element; wherein each of said groupings has a grouping sizeequal to said visualizer size; averaging said variable for each elementin a like position of all of said groupings to obtain a compositedetection success value; and displaying detection success values by aplurality of visualizer-coincidence pixels having a size equal to saidvisualizer size, each said visualizer-coincidence pixel having a samecolor as said corresponding visualizer pixel when said correspondingsuccess value indicates detection success and another color otherwise.45. A computer program product comprising a computer usable mediumhaving computer readable program code means embodied therein for causinga watermark to be imparted into an image, the computer readable programcode means in said computer program product comprising computer readableprogram code means for causing a computer to effect the steps ofclaim
 1. 46. A computer program product comprising a computer usablemedium having computer readable program code means embodied therein forcausing a watermark to be imparted into an image, the computer readableprogram code means in said computer program product comprising computerreadable program code means for causing a computer to effect the stepsof claim
 5. 47. A computer program product comprising a computer usablemedium having computer readable program code means embodied therein forcausing a watermark to be imparted into an image, the computer readableprogram code means in said computer program product comprising computerreadable program code means for causing a computer to effect the stepsof claim
 11. 48. A computer program product comprising a computer usablemedium having computer readable program code means embodied therein forcausing generation of a watermarked image, the computer readable programcode means in said computer program product comprising computer readableprogram code means for causing a computer to effect the steps of claim13.
 49. A computer program product comprising a computer usable mediumhaving computer readable program code means embodied therein for causingformation of a watermarking plane, the computer readable program codemeans in said computer program product comprising computer readableprogram code means for causing a computer to effect the steps of claim14.
 50. An article of manufacture comprising a computer usable mediumhaving computer readable program code means embodied therein for causingdetection of a watermark in a marked image, the computer readableprogram code means in said article of manufacture comprising computerreadable program code means for causing a computer to effect the stepsof claim
 15. 51. An article of manufacture comprising a computer usablemedium having computer readable program code means embodied therein forcausing detection of a watermark in a marked image, the computerreadable program code means in said article of manufacture comprisingcomputer readable program code means for causing a computer to effectthe steps of claim
 16. 52. An article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing generation of a visual representation of adata array of data elements, the computer readable program code means insaid article of manufacture comprising computer readable program codemeans for causing a computer to effect the steps of claim
 39. 53. Anarticle of manufacture comprising a computer usable medium havingcomputer readable program code means embodied therein for causing awatermark to be imparted onto a digitized image, the computer readableprogram code means in said article of manufacture comprising computerreadable program code means for causing a computer to effect the stepsof claim
 18. 54. An article of manufacture comprising a computer usablemedium having computer readable program code means embodied therein forcausing a watermark to be imparted onto a digitized image, the computerreadable program code means in said article of manufacture comprisingcomputer readable program code means for causing a computer to effectthe steps of claim
 19. 55. An article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing detection of a watermark imparted onto adigitized image, the computer readable program code means in saidarticle of manufacture comprising computer readable program code meansfor causing a computer to effect the steps of claim
 20. 56. An articleof manufacture comprising a computer usable medium having computerreadable program code means embodied therein for causing detection of awatermark in a marked image, the computer readable program code means insaid article of manufacture comprising computer readable program codemeans for causing a computer to effect the steps of claim
 30. 57. Anarticle of manufacture comprising a computer usable medium havingcomputer readable program code means embodied therein for causinggeneration of a visual representation of a data array of data elements,the computer readable program code means in said article of manufacturecomprising computer readable program code means for causing a computerto effect the steps of claim
 39. 58. An article of manufacturecomprising a computer usable medium having computer readable programcode means embodied therein for causing demonstration of an existence ofa watermark in a marked image, the computer readable program code meansin said article of manufacture comprising computer readable program codemeans for causing a computer to effect the steps of claim
 43. 59. Acomputer program product comprising a computer usable medium havingcomputer readable program code means embodied therein for causingdetection of a watermark in a marked image, the computer readableprogram code means in said computer program product comprising computerreadable program code means for causing a computer to effect the stepsof claim
 44. 61. An apparatus to impart a watermark onto a digitizedimage, said apparatus comprising mechanisms for implementing the methodof claim
 1. 62. An apparatus for imparting a watermark onto a digitizedimage comprising mechanisms for implementing the method of claim
 5. 63.An apparatus for imparting a watermark onto a digitized image comprisingmechanisms for implementing the method of claim
 6. 64. An apparatus forimparting a watermark onto a digitized image comprising mechanisms forimplementing the method of claim
 11. 65. A method for detecting awatermark in a marked image, said method comprising: providing saidmarked image having said watermark; altering said marked image employinga blurring filter in producing a filtered image; and employing awatermark detection method upon said filtered image to detect saidwatermark.
 66. A method for detecting a watermark in a marked image,said method comprising: providing said marked image having saidwatermark; processing the marked image and producing a screened image;altering said screened image employing a blurring filter in producing afiltered image; and employing a watermark detection method upon saidfiltered image to detect said watermark.
 67. A method as recited inclaim 66, wherein the step of processing includes producing a derivativeimage by screening, printing and scanning the marked image.
 68. A methodas recited in claim 15, wherein the step of aligning includes alteringsaid marked image employing a blurring filter.
 69. A method as recitedin claim 16, wherein the step of aligning includes altering said markedimage employing a blurring filter.
 70. A method as recited in claim 20,wherein the step of aligning includes altering said marked imageemploying a blurring filter.
 71. A method as recited in claim 30,wherein the step of providing includes altering said marked imageemploying a blurring filter.
 72. A method as recited in claim 44,wherein the step of aligning includes altering said marked imageemploying a blurring filter.
 73. An article of manufacture as recited inclaim 51, wherein the step of aligning includes altering said markedimage employing a blurring filter.
 74. An article of manufacture asrecited in claim 59, wherein the step of aligning includes altering saidmarked image employing a blurring filter.
 75. An apparatus as recited inclaim 62, wherein the means of providing includes means for alteringsaid marked image employing a blurring filter.
 76. A method ofgenerating a visual representation of a data array of data elementshaving a data array size, said method comprising: providing a visualizerpattern of visualizer pixels represented by a visualizer array ofvisualizer elements, said visualizer array having a visualizer arraysize equal to said data array size, wherein each of said visualizerelements has a first logical value if a corresponding visualizer pixelis a first color and a complementary logical value if said correspondingvisualizer pixel has a second color; forming a data image of imagepixels represented by an image array having an image array size equal tosaid data array size, wherein an image pixel has a corresponding dataelement and a corresponding visualizer pixel; setting said data pixel toa color of said corresponding visualizer pixel if a value of said dataelement is above a predetermined threshold and to another color if saidvalue is below said predetermined threshold; and displaying said dataimage to form said visual representation.
 77. A method as recited inclaim 76, wherein said data array represents data resulting from awatermark detection implementation.
 78. A method as recited in claim 76,wherein said first color is black and said second color is white.
 79. Amethod as recited in claim 76, wherein said threshold is set at a fiftypercent success rate.
 80. An article of manufacture comprising acomputer usable medium having computer readable program code meansembodied therein for causing generation of a visual representation of adata array of data elements, the computer readable program code means insaid article of manufacture comprising computer readable program codemeans for causing a computer to effect the steps of claim
 76. 81. Acomputer program product comprising a computer usable medium havingcomputer readable program code means embodied therein for causinggeneration of a visual representation of a data array of data elements,the computer readable program code means in said computer programproduct comprising computer readable program code means for causing acomputer to effect the steps of claim
 76. 82. An apparatus forgenerating a watermarked image comprising mechanisms for implementingthe method of claim
 13. 83. An apparatus comprising mechanisms forimplementing the method of claim
 14. 84. An apparatus for detecting awatermark in a marked image comprising mechanisms for implementing themethod of claim
 15. 85. An apparatus for detecting a watermarking planecomprising mechanisms for implementing the method of claim
 16. 86. Anapparatus for imparting a watermark onto a digitized image comprisingmechanisms for implementing the method of claim
 19. 87. An apparatus fordetecting a watermark comprising mechanisms for implementing the methodof claim
 20. 88. An apparatus for detecting a watermark comprisingmechanisms for implementing the method of claim
 30. 89. An apparatus fordemonstrating an existence of a watermark in a marked image comprisingmechanisms for implementing the method of claim
 43. 90. An apparatus fordetecting a watermark comprising mechanisms for implementing the methodof claim 44
 91. A method for detecting a watermarking plane comprisingthe steps of: providing an image having a plurality of image pixels,u(i, j), with said image having I rows and J columns, and a pixel in rowi and column j having at least one component, marked by a watermarkingplane; said watermarking plane having a plurality of watermarkingelements, w(i, j), with said watermarking plane having I rows and Jcolumns, and an element in row i and column j having a brightnessmultiplying factor; aligning said watermarking plane with said image;identifying a subset of said image elements; and for each pixel, u(i,j), of said subset of image pixels, employing a detection scheme indetermining a probability of watermark detection based on a property ofuniform distribution of the random brightness multiplying factors or therandom brightness adding or subtracting factors.